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Polynomial growth of the codimensions sequence of algebras with group graded involution

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Abstract

An algebra graded by a group G and endowed with a graded involution * is called a (G, *)-algebra. Here we consider G a finite abelian group and classify the subvarieties of the varieties of almost polynomial growth generated by finite-dimensional (G, *)-algebras. Also, we present, up to equivalence, the complete list of (G, *)-algebras generating varieties of at most linear growth. Along the way, we give a new characterization of varieties of polynomial growth generated by finite-dimensional (G, *)-algebras by considering the structure of the generating algebra.

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Acknowledgement

The authors would like to thank the referee for various suggestions.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Avenida Antonio Carlos 6627, 31123-970, Belo Horizonte, Brazil

    Maralice Assis de Oliveira, Rafael Bezerra dos Santos & Ana Cristina Vieira

Authors
  1. Maralice Assis de Oliveira
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  2. Rafael Bezerra dos Santos
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  3. Ana Cristina Vieira
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Corresponding author

Correspondence to Ana Cristina Vieira.

Additional information

Partially supported by CAPES.

Partially supported by FAPEMIG, grant numbers APQ-01801-21 and RED-00133-21.

Partially supported by CNPq.

Partially supported by FAPEMIG, grant numbers APQ-01248-18 and RED-00133-21.

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de Oliveira, M.A., dos Santos, R.B. & Vieira, A.C. Polynomial growth of the codimensions sequence of algebras with group graded involution. Isr. J. Math. (2023). https://doi.org/10.1007/s11856-023-2585-6

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  • DOI: https://doi.org/10.1007/s11856-023-2585-6

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