Non-commutative Hom-Poisson algebras

Abstract

A Hom-type generalization of non-commutative Poisson algebras, called non-commutative Hom-Poisson algebras, are studied. They are closed under twisting by suitable self-maps. Hom-Poisson algebras, in which the Hom-associative product is commutative, are closed under tensor products. Through (de)polarization Hom-Poisson algebras are equivalent to admissible Hom-Poisson algebras, each of which has only one binary operation. Multiplicative admissible Hom-Poisson algebras are Hom-power associative.

23 pages

References in corpus (8)

• Deformation quantization of Poisson manifolds, I
• Vertex Algebras and Algebraic Curves
• Deformations of Lie Algebras using $\sigma$-derivations
• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Cohomology and Deformation of Leibniz Pairs
• Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
• Hom-power associative algebras

Cited by in corpus (11)

• Hom-Lie algebroids
• Twisting Poisson algebras, coPoisson algebras and Quantization
• A twisted generalization of Novikov-Poisson algebras
• On Hom-Lie antialgebra
• Hom-alternative modules and Hom-Poisson comodules
• (Non-BiHom-Commutative) BiHom-Poisson algebras
• Representations and relative Rota-Baxter operators of Hom-Leibniz Poisson algebras
• Some structures of Hom-Poisson color algebras
• Structures of BiHom-Poisson algebras
• BiHom-Poisson color algebras
• Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras