Abstract
We propose an algebraic viewpoint of the problem of deformation quantization of the so-called almost Poisson algebras, which are algebras with a commutative associative product and an antisymmetric bracket which is a biderivation but does not necessarily satisfy the Jacobi identity. From that viewpoint, the main result of the paper asserts that, by contrast with Poisson algebras, the only reasonable category of algebras in which almost Poisson algebras can be quantized is isomorphic to the category of almost Poisson algebras itself, and the trivial two-term quantization formula already gives a solution to the quantization problem.
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Acknowledgements
I am grateful to Ivan Pavlovich Shestakov for discussions of Kokoris algebras and general encouragement, and to Dmitry Vassilevich for some inspiring conversations. The first draft of this note was completed during the author’s visit to Tashkent by invitation of Farkhod Eshmatov, and the author is grateful to him for warm hospitality.
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The author was supported by Institut Universitaire de France and by FAPESP (grant 2022/10933-3).
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Dotsenko, V. Identities for deformation quantizations of almost Poisson algebras. Lett Math Phys 114, 4 (2024). https://doi.org/10.1007/s11005-023-01748-x
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DOI: https://doi.org/10.1007/s11005-023-01748-x