Deformation Quantization of Nonassociative Algebras

Elisabeth Remm ()
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Elisabeth Remm: IRIMAS UR 7499, Université de Haute-Alsace, 68093 Mulhouse Cedex, France

Mathematics, 2024, vol. 13, issue 1, 1-35

Abstract: We investigate formal deformations of certain classes of nonassociative algebras including classes of K [ Σ 3 ] -associative algebras, Lie-admissible algebras and anti-associative algebras. In a process which is similar to Poisson algebra for the associative case, we identify for each type of algebras ( A , μ ) a type of algebras ( A , μ , ψ ) such that formal deformations of ( A , μ ) appear as quantizations of ( A , μ , ψ ) . The process of polarization/depolarization associates to each nonassociative algebra a couple of algebras which products are respectively commutative and skew-symmetric and it is linked with the algebra obtained from the formal deformation. The anti-associative case is developed with a link with the Jacobi–Jordan algebras.

Keywords: nonassociative algebras; deformation quantization; polarization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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