Abstract
In this paper we introduce color Hom-Poisson algebras and show that every color Hom-associative algebra has a non-commutative Hom-Poisson algebra structure in which the Hom-Poisson bracket is the commutator bracket. Then we show that color Poisson algebras (respectively morphism of color Poisson algebras) turn to color Hom-Poisson algebras (respectively morphism of Color Hom-Poisson algebras) by twisting the color Poisson structure. Next we prove that modules over color Hom–associative algebras A extend to modules over the color Hom-Lie algebras L(A), where L(A) is the color Hom-Lie algebra associated to the color Hom-associative algebra A. Moreover, by twisting a color Hom-Poisson module structure map by a color Hom-Poisson algebra endomorphism, we get another one.
Highlights
Color Hom-Poisson algebras are generalizations of Hom-Poisson algebras introducedin [1], where they emerged naturally in the study of 1-parameter formaldeformations of commutative Hom-associative algebras
Color Hom-Poisson algebrasgeneralize, on the one hand, color Hom-associative [2,3] and color Hom-Lie algebras[2,3] which have been recently investigated by various authors
The aim of this paper is to study color Hom-Poisson algebras and modules over color Hom-Poisson algebras
Summary
Color Hom-Poisson algebras are generalizations of Hom-Poisson algebras introducedin [1], where they emerged naturally in the study of 1-parameter formaldeformations of commutative Hom-associative algebras. Color Hom-Poisson algebrasgeneralize, on the one hand, color Hom-associative [2,3] and color Hom-Lie algebras[2,3] which have been recently investigated by various authors. Onthe other hand, they generalize Hom-Lie superalgebras [4]. The aim of this paper is to study color Hom-Poisson algebras and modules over color Hom-Poisson algebras. Va We denote H (V) the set of all homogeneous elements in V
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