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Condition (S+) in ranks 4, 8, and 9 J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-24 Nicholas M. Katz, Pham Huu Tiep
Condition , introduced in , plays a key role in the study of Kloosterman and hypergeometric -adic local systems in positive characteristic . Prior results of , establish for primitive Kloosterman and hypergeometric sheaves, except possibly in ranks 4, 8, and 9. In this paper we study in these remaining ranks, and completely determine when does or does not hold.
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Semi-abelian condition for color Hopf algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-24 Andrea Sciandra
Recently, in , it was shown that the category of cocommutative Hopf algebras over an arbitrary field is semi-abelian. We extend this result to the category of cocommutative color Hopf algebras, i.e. of cocommutative Hopf monoids in the symmetric monoidal category of -graded vector spaces with an abelian group, given an arbitrary skew-symmetric bicharacter on , when is finitely generated and the characteristic
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Computads for generalised signatures J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-24 Ioannis Markakis
We introduce a notion of signature whose sorts form a direct category, and study computads for such signatures. Algebras for such a signature are presheaves with an interpretation of every function symbol of the signature, and we describe how computads give rise to signatures. Motivated by work of Batanin, we show that computads with certain generator-preserving morphisms form a presheaf category,
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Descent conditions for generation in derived categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-21 Pat Lank
This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian scheme is preserved by the derived pushforward of a proper morphism. Consequently, we can produce upper bounds on the Rouquier dimension of the bounded derived category, and applications concerning affine varieties are studied. In the process, a necessary and sufficient constraint
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Wide subcategories of a domestic weighted projective line J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-19 Yiyu Cheng
For a weighted projective line , a wide subcategory of the category of coherent sheaves over is called -invariant if it is closed under the grading shift of the canonical element . We proved that a -invariant wide subcategory of containing a vector bundle is the perpendicular category of a torsion exceptional sequence. If is of domestic type, then the poset of wide subcategories of is the union of
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Reflexive modules over the endomorphism algebras of reflexive trace ideals J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-19 Naoki Endo, Shiro Goto
In the present paper we investigate reflexive modules over the endomorphism algebras of reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem generalizes both of the results of S. Goto, N. Matsuoka, and T. T. Phuong () and T. Kobayashi () concerning the endomorphism algebra of its maximal ideal. We also explore the question of when the category of reflexive modules
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A monoidal Dold-Kan correspondence for comodules J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-19 Maximilien Péroux
Cofibrantly generated model categories are generalizations of CW-approximations which provide an inductive cofibrant replacement. We provide examples of inductive fibrant replacements constructed as Postnikov towers for simplicial and differential graded comodules. Our main application is to show that simplicial comodules and connective differential graded comodules are Quillen equivalent and their
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Degree of the 3-secant variety J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-18 Doyoung Choi
In this paper, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 5-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of the double point formula to reduce the calculation into the case of the 2-secant variety. As a resolution of the 2-secant variety
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Modules with finitely generated cohomology, and singularities of C⁎BG J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-18 David J. Benson, John Greenlees
Let be a finite group and a field of characteristic . We conjecture that if is a -module with finitely generated as a module over then as an element of the stable module category , is contained in the thick subcategory generated by the finitely generated -modules and the modules with .
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On 2-categorical ∞-cosmoi J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-18 John Bourke, Stephen Lack
Recently Riehl and Verity have introduced ∞-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those ∞-cosmoi which are in fact 2-categories; we shall refer to these as 2-cosmoi.
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Internal sums for synthetic fibered (∞,1)-categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-18 Jonathan Weinberger
We give structural results about bifibrations of (internal) -categories with internal sums. This includes a higher version of Moens' Theorem, characterizing cartesian bifibrations with extensive stable and disjoint internal sums over lex bases as Artin gluings of lex functors. We also treat a generalized version of Moens' Theorem due to Streicher which does not require the Beck–Chevalley condition
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Algebraic properties of binomial edge ideals of Levi graphs associated with curve arrangements J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-15 Rupam Karmakar, Rajib Sarkar, Aditya Subramaniam
In this article, we study algebraic properties of binomial edge ideals of Levi graphs associated with certain plane curve arrangements. Using combinatorial properties of Levi graphs, we discuss the Cohen-Macaulayness of binomial edge ideals of Levi graphs associated to some curve arrangements in the complex projective plane, like the -arrangement of curves and the conic-line arrangements. We also discuss
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Injectivity and projectivity domains of a simple module over a commutative ring J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-15 Rachid Tribak
Let be a commutative ring. We determine the cyclic modules in the projectivity domain and those in the injectivity domain of a simple -module. An -module is called poor (p-poor) if for every -module , is -injective ( is -projective) only if is semisimple. We describe the structure of simple poor -modules and simple p-poor -modules. We show that every simple poor -module is p-poor and the converse holds
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Construction and finite generation of the strict closure of rings J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-15 Ryotaro Isobe
The construction of Arf rings and strictly closed rings has been studied widely; however, there has been no clear description of the structure of the strict closure when is not a finitely generated -module. In this paper, we investigate the construction and finite generation of the strict closure of rings. We determine its structure when is a Cohen-Macaulay semi-local ring of dimension one, with for
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On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4 J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-13 Đặng Võ Phúc
Let denote the Steenrod algebra over the field of characteristic two, . Singer's algebraic transfer, introduced by Singer in his work (Singer (1989) ), is a rather effective tool for unraveling the intricate structure of the mod-two cohomology of the Steenrod algebra, . In the present study, we aim to investigate the behavior of this algebraic transfer for rank five in the generic family of internal
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Quotient toposes of discrete dynamical systems J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-09 Ryuya Hora, Yuhi Kamio
Lawvere's open problem on quotient toposes has been solved for boolean Grothendieck toposes but not for non-boolean toposes. As a simple and non-trivial example of a non-boolean topos, this paper provides a complete classification of the quotient toposes of the topos of discrete dynamical systems, which, in this context, are sets equipped with an endofunction. This paper also offers an order-theoretic
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Waring problem for matrices over finite fields J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-07 Krishna Kishore, Adrian Vasiu, Sailun Zhan
We prove that for all integers , , and , every matrix in is a sum of two kth powers: . We further generalize and refine this result in the cases when both and can be chosen to be invertible, cyclic, or split semisimple, when is coprime to , or when is sufficiently large. We also give a criterion for the Waring problem in terms of stabilizers.
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Ordered locales J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-07 Chris Heunen, Nesta van der Schaaf
We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called condition, and the newly defined category of . The adjunction restricts to an equivalence of categories between spatial ordered locales and sober -ordered spaces with open cones.
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Hopf-Galois structures on separable field extensions of degree pq J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-07 Andrew Darlington
In 2020, Alabdali and Byott described the Hopf-Galois structures arising on Galois field extensions of squarefree degree. Extending to squarefree separable, but not necessarily normal, extensions is a natural next step. One must consider now the interplay between two Galois groups and , where is the Galois closure of . In this paper, we give a characterisation and enumeration of the Hopf-Galois structures
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Normal subalgebras of a polynomial ring J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-06 R.V. Gurjar, M. Miyanishi
Let be a finitely generated subalgebra of a polynomial ring over the complex field . Assuming that is normal, we clarify the structure of under additional assumptions if . If and is regular, then Spec has an -fibration over or with restrictions on the number of multiple fibers (see Theorem 3). If , we assume that is cofinite, i.e., is a finite -module, and contains a coordinate . Then either is a polynomial
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Quantum traces for [formula omitted]: The case n = 3 J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-05 Daniel C. Douglas
We generalize Bonahon–Wong's -quantum trace map to the setting of . More precisely, given a non-zero complex parameter , we associate to each isotopy class of framed oriented links in a thickened punctured surface a Laurent polynomial in -deformations of the Fock–Goncharov -coordinates for higher Teichmüller space. This construction depends on a choice of ideal triangulation of the surface . Along
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Powerful 3-Engel groups J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-28 Iker de las Heras, Marialaura Noce, Gunnar Traustason
In this paper we study finite powerful 3-Engel groups. In particular, we find sharp upper bounds for the nilpotency class of finite powerful 3-Engel groups and in the subclass of finite powerful metabelian 3-Engel groups.
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Ideal classes of orders in quaternion algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Stefano Marseglia, Harry Smit, John Voight
We provide an algorithm that, given any order in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right -ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras.
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Homological dimensions of Burch ideals, submodules and quotients J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Dipankar Ghosh, Aniruddha Saha
The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this article is to characterize various local rings in terms of homological invariants of Burch ideals, Burch submodules, or that of the corresponding quotients. Specific applications of our results include the following: Let be a commutative
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Vertex operators for imaginary [formula omitted] subalgebras of the Monster Lie algebra J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Darlayne Addabbo, Lisa Carbone, Elizabeth Jurisich, Maryam Khaqan, Scott H. Murray
The Monster Lie algebra is a quotient of the physical space of the vertex algebra , where is the Moonshine module vertex operator algebra of Frenkel, Lepowsky, and Meurman, and is the vertex algebra corresponding to the rank 2 even unimodular lattice . We construct vertex algebra elements that project to bases for subalgebras of isomorphic to , corresponding to each imaginary simple root, denoted for
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Gröbner geometry for regular nilpotent Hessenberg Schubert cells J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Mike Cummings, Sergio Da Silva, Megumi Harada, Jenna Rajchgot
A regular nilpotent Hessenberg Schubert cell is the intersection of a regular nilpotent Hessenberg variety with a Schubert cell. In this paper, we describe a set of minimal generators of the defining ideal of a regular nilpotent Hessenberg Schubert cell in the type setting. We show that these minimal generators are a Gröbner basis for an appropriate lexicographic monomial order. As a consequence, we
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On the generating function and growth of the positive singular braid monoid J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-22 A.L. Anisimov, G.A. Kameneva, V.V. Vershinin
We give an elementary proof of the fact that the generating function of the positive singular braid monoid is rational and we give the exact formula for such monoid on three strands.
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Injectives over Leavitt path algebras of graphs with disjoint cycles J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-21 Gene Abrams, Francesca Mantese, Alberto Tonolo
Let be any field, and let be a finite graph with the property that every vertex in is the base of at most one cycle (i.e., a graph with disjoint cycles). We explicitly construct the injective envelope of each simple left module over the Leavitt path algebra . The main idea girding our construction is that of a “formal power series” extension of modules, thereby developing for all graphs with disjoint
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Vopěnka's principle in ∞-categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-20 Giulio Lo Monaco
In this article, the interplay between Vopěnka's principle, as well as its weaker counterpart, and presentable ∞-categories is studied. Analogous statements, arising after replacing categories with ∞-categories in the original ones, are introduced and compared to these. Further, the attention is focused on the question of to what extent the consequences that (weak) Vopěnka's principle have on the detection
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On the behavior of Massey products under field extension J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-20 Aleksandar Milivojević
We show that global vanishing of Massey products on a commutative differential graded algebra is not invariant under field extension. Non-vanishing triple Massey products remain non-vanishing upon field extension, while higher Massey products can generally vanish. If the field being extended is algebraically closed, all non-vanishing Massey products remain non-vanishing on a finite type commutative
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On the obscure axiom for one-sided exact categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-19 Ruben Henrard, Adam-Christiaan van Roosmalen
One-sided exact categories are obtained via a weakening of a Quillen exact category. Such one-sided exact categories are homologically similar to Quillen exact categories: a one-sided exact category can be (essentially uniquely) embedded into its exact hull ; this embedding induces a derived equivalence .
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Combinatorial mutations of Gelfand–Tsetlin polytopes, Feigin–Fourier–Littelmann–Vinberg polytopes, and block diagonal matching field polytopes J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-19 Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
The Gelfand-Tsetlin and the Feigin–Fourier–Littelmann–Vinberg polytopes for the Grassmannians are defined, from the perspective of representation theory, to parametrize certain bases for highest weight irreducible modules. These polytopes are Newton-Okounkov bodies for the Grassmannian and, in particular, the GT polytope is an example of a string polytope. The polytopes admit a combinatorial description
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Line bundles on G-Bott-Samelson-Demazure-Hansen varieties J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-15 Saurav Bhaumik, Pinakinath Saha
Let be a semi-simple simply connected algebraic group over an algebraically closed field of arbitrary characteristic. Let be a Borel subgroup of containing a maximal torus of . Let be the Weyl group of with respect to . For an arbitrary sequence of simple reflections in , let be the Bott-Samelson-Demazure-Hansen variety (BSDH-variety for short) corresponding to . Let denote the fibre bundle on whose
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Equivalence of v-decomposition matrices for blocks of Ariki-Koike algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-15 Alice Dell'Arciprete
We consider the representation theory of the Ariki-Koike algebra, a -deformation of the group algebra of the complex reflection group . We examine blocks of the Ariki-Koike algebra. In particular, we prove a sufficient condition such that restriction of modules leads to a natural correspondence between the multipartitions of whose Specht modules belong to a block and those of whose Specht modules belong
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Shapovalov elements of classical and quantum groups J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-13 Andrey Mudrov
Shapovalov elements of the classical or quantized universal enveloping algebra of a simple Lie algebra are parameterized by a positive root and a positive integer . They relate the highest vector of a reducible Verma module with highest vectors of its submodules. We obtain a factorization of to a product of and calculate as a residue of a matrix element of the inverse Shapovalov form via a generalized
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A Molev-Sagan type formula for double Schubert polynomials J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-12 Matthew J. Samuel
We give a Molev-Sagan type formula for computing the product of two double Schubert polynomials in different sets of coefficient variables where the descents of and satisfy certain conditions that encompass Molev and Sagan's original case and conjecture positivity in the general case. Additionally, we provide a Pieri formula for multiplying an arbitrary double Schubert polynomial by a factorial elementary
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On the degree of varieties of sum of squares J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-10 Andrew Ferguson, Giorgio Ottaviani, Mohab Safey el Din, Ettore Teixeira Turatti
We study the problem of how many different sum of squares decompositions a general polynomial with SOS-rank admits. We show that there is a link between the variety of all SOS-decompositions of and the orthogonal group . We exploit this connection to obtain the dimension of and show that its degree is bounded from below by the degree of . In particular, for we show that is isomorphic to and hence the
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Sum of squares decomposition of positive polynomials with rational coefficients J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-09 Santiago Laplagne
We present an example of a strictly positive polynomial with rational coefficients that can be decomposed as a sum of squares of polynomials over but not over . This answers an open question by C. Scheiderer posed as the second question in . We verify that the example we construct defines a nonsingular projective hypersurface, giving also a positive answer to the third question posed in that section
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On a bijection between a finite group and cyclic group J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-01 Mohsen Amiri
We show that for any finite group of order there exists a bijection from onto the cyclic group such that divides for all . This confirms Problem 18.1 in .
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On some central operators for loop Lie superalgebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-01 Sudipta Mukherjee, Santosha Pattanayak, Sachin S. Sharma
Let be either a basic classical Lie superalgebra or over the field of complex numbers . For any associative, commutative, and finitely generated algebra with unity, we consider the loop Lie superalgebra . In , Rao defined a class of central operators for and conjectured that these central operators, which generalizes the classical Gelfand invariants, generate the algebra for . In this article we prove
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Naturality of the ∞-categorical enriched Yoneda embedding J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Shay Ben-Moshe
We make Hinich's ∞-categorical enriched Yoneda embedding natural. To do so, we exhibit it as the unit of a partial adjunction between the functor taking enriched presheaves and Heine's functor taking a tensored category to an enriched category. Furthermore, we study a finiteness condition of objects in a tensored category called being atomic, and show that the partial adjunction restricts to a (non-partial)
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A variant of the effective adjunction conjecture with applications J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Zhan Li
We introduce a variant of the effective adjunction conjecture for lc-trivial fibrations. This variant is suitable for inductions and can be used to treat real coefficients.
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On skew partial derivatives and a Hermite-type interpolation problem J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Jonathan Armando Briones Donoso, Andrea Luigi Tironi
Let R:=F[x;σ,δ] be a multivariate skew polynomial ring over a division ring F. In this paper, we introduce the notion of right and left (σ,δ)-partial derivatives of polynomials in R and we prove some of their main properties. As an application of these results, we solve in R a Hermite-type multivariate skew polynomial interpolation problem. The main technical tools and results used here are of constructive
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Semilinear idempotent distributive ℓ-monoids J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Simon Santschi
We prove a representation theorem for totally ordered idempotent monoids via a nested sum construction. Using this representation theorem we obtain a characterization of the subdirectly irreducible members of the variety of semilinear idempotent distributive ℓ-monoids and a proof that its lattice of subvarieties is countably infinite. For the variety of commutative idempotent distributive ℓ-monoids
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Automorphisms of weighted projective hypersurfaces J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Louis Esser
We prove several results concerning automorphism groups of quasismooth complex weighted projective hypersurfaces; these generalize and strengthen existing results for hypersurfaces in ordinary projective space. First, we prove in most cases that automorphisms extend to the ambient weighted projective space. We next provide a characterization of when the linear automorphism group is finite and find
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Koszul modules of Kac-Moody Lie algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Tymoteusz Chmiel
We introduce Koszul modules associated with (graded) Kac-Moody Lie algebras. We provide a precise criterion for when these modules are of finite length. As an exemplary application we deduce a bound on the dimension of the second graded component for a certain class of graded Kac-Moody Lie algebras. We also provide an exact description of all nilpotent Kac-Moody Koszul modules.
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A homotopy coherent nerve for (∞,n)-categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Lyne Moser, Nima Rasekh, Martina Rovelli
In the case of -categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories. This shows that homotopy coherent diagrams of -categories can equivalently be defined as functors of quasi-categories or as simplicially enriched functors out of the homotopy coherent categorifications.
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An analogue of Stone duality via support J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Henning Krause
The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. In particular, the parallel between support via closed and open sets is addressed in terms of Hochster duality. As an application we indicate some consequences for tensor exact categories
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Magnetic fields on non-singular 2-step nilpotent Lie groups J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Gabriela P. Ovando, Mauro Subils
This work has a twofold purpose - the existence study of closed 2-forms, known as magnetic fields, on 2-step nilpotent Lie groups and generating examples for the non-singular family. At the Lie algebra level, while the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the existence of closed 2-forms for which the center is
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The magnitude for Nakayama algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Dawei Shen, Yaru Wu
The magnitude for algebras is a generalization of the Euler characteristic. We investigate the magnitude for Nakayama algebras. Using Ringel's resolution quiver, the existence and the value of rational magnitude is given. As a result, we show directly that the finite global dimension criteria for Nakayama algebras of Madsen and the first author are equivalent.
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Commutative subalgebra of a shuffle algebra associated with quantum toroidal glm|n J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-19 B. Feigin, M. Jimbo, E. Mukhin
We define and study the shuffle algebra Shm|n of the quantum toroidal algebra Em|n associated to Lie superalgebra glm|n. We show that Shm|n contains a family of commutative subalgebras Bm|n(s) depending on parameters s=(s1,…,sm+n), ∏isi=1, given by appropriate regularity conditions. We show that Bm|n(s) is a free polynomial algebra and give explicit generators which conjecturally correspond to the
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A certain twisted Jacquet module of GL(6) over a finite field: The rank 2 case J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Kumar Balasubramanian, Himanshi Khurana
Let F be a finite field and G=GL(6,F). In this paper, we explicitly describe the structure of the twisted Jacquet module πN,ψA where A is a rank 2 matrix and π is an irreducible cuspidal representation of G.
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Invariants of non-isolated singularities of hypersurfaces J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Yotam Svoray
In this paper we generalize some results by Siersma, Pellikaan, and de Jong regarding morsifications of singular hypersurfaces whose singular locus is a smooth curve, and present some applications to the study of Yomdin-type isolated singularities. In order to prove these results, we discuss the transversal discriminant of such singularities and how it relates to other algebraic and topological invariants
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Cellular resolutions of monomial ideals and their Artinian reductions J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Sara Faridi, Mohammad D.G. Farrokhi D.G., Roya Ghorbani, Ali Akbar Yazdan Pour
The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-complexes? Velasco gave families of examples of monomial ideals that do not have minimal cellular resolutions, but those examples have large minimal generating sets. In this paper, we show that if a monomial ideal has at most
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Indecomposable integrally closed modules of rank 3 over two-dimensional regular local rings J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Futoshi Hayasaka, Vijay Kodiyalam
We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank three.
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Modified Makar-Limanov and Derksen invariants J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Sergey Gaifullin, Anton Shafarevich
We investigate modified Makar-Limanov and Derksen invariants of an affine algebraic variety. The modified Makar-Limanov invariant is the intersection of kernels of all locally nilpotent derivations with slices and the modified Derksen invariant is the subalgebra generated by these kernels. We prove that the modified Makar-Limanov invariant coincides with the Makar-Limanov invariant if there exists
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Characterizations of tame algebras with separating families of almost cyclic coherent components J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Piotr Malicki
We provide new characterizations of tame algebras with separating families of almost cyclic coherent Auslander–Reiten components in terms of the support of the indecomposable modules, the minimum coordinates of dimension vectors of the indecomposable modules and the values of the Tits quadratic form.
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A refined scissors congruence group and the third homology of SL2 J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-15 Behrooz Mirzaii, Elvis Torres Pérez
There is a natural connection between the third homology of SL2(A) and the refined Bloch group RB(A) of a commutative ring A. In this article we investigate this connection and as the main result we show that if A is a universal GE2-domain such that −1∈A×2, then we have the exact sequenceH3(SM2(A),Z)→H3(SL2(A),Z)→RB(A)→0, where SM2(A) is the group of monomial matrices in SL2(A). Moreover, we show that