Modules Over Color Hom-Poisson Algebras
Department de Mathematiques, UJNK/Centre Universitaire de N'Zerekore, BP: 50, N’Zerekore, Guinea
- *Corresponding Author:
- Ibrahima Bakayoko,
Department de Mathematiques,
UJNK/Centre Universitaire de N'Zerekore, BP: 50, N’Zerekore, Guinea,
E-mail: [email protected]
Received date: August 12, 2013; Accepted date: September 30, 2014; Published date: October 06, 2014
Citation: Bakayoko I (2014) Modules Over Color Hom-Poisson Algebras. J Generalized Lie Theory Appl 8:212. doi:10.4172/1736-4337.1000212
Copyright: © 2014 Bakayoko I. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.