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Deformation Quantization of Nonassociative Algebras

Author

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  • Elisabeth Remm

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

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.

Suggested Citation

  • Elisabeth Remm, 2024. "Deformation Quantization of Nonassociative Algebras," Mathematics, MDPI, vol. 13(1), pages 1-35, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:58-:d:1554734
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