Journal of Generalized Lie Theory and Applications

Modules Over Color Hom-Poisson Algebras

Ibrahima Bakayoko

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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.

Article information

Source
J. Gen. Lie Theory Appl., Volume 8, Number 1 (2014), 6 pages.

Dates
First available in Project Euclid: 23 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1437658041

Digital Object Identifier
doi:10.4172/1736-4337.1000212

Mathematical Reviews number (MathSciNet)
MR3620395

Zentralblatt MATH identifier
1332.17026

Keywords
Color hom-associative algebras Color hom-Lie algebras Homomorphism Formal deformation Hom-modules Modules over color Hom-Lie algebras Modules over color Hom-Poisson algebras

Citation

Bakayoko, Ibrahima. Modules Over Color Hom-Poisson Algebras. J. Gen. Lie Theory Appl. 8 (2014), no. 1, 6 pages. doi:10.4172/1736-4337.1000212. https://projecteuclid.org/euclid.jglta/1437658041


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