Ibrahima Bakayoko — Page 2

arXiv2016

Hom-alternative modules and Hom-Poisson comodules

In this paper we introduce modules over both left and right Hom-alternative algebras. We give some constructions of left and right Hom-alternative modules and give various properties of both, as well as examples. Then, we prove that morphisms of left alternative algebras extend to morphisms of left Hom-alternative algebras. Next, we introduce comodules over Hom-Poisson coalgebras and show that we may obtain a structure map of a comodule over a Hom-Poisson coalgebra from a given one.

math.RA↗

arXiv2014

Color Hom-Akivis algebras, Color Hom-Leibniz algebras and Modules over Color Hom-Leibniz algebras

In this paper we introduce color Hom-Akivis algebras and prove that the commutator of any color non-associative Hom-algebra structure map leads to a color Hom-akivis algebra. We give various constructions of color Hom-Akivis algebras. Next we study flexible and alternative color Hom-Akivis algebras. Likewise color Hom-Akivis algebras, we introduce non-commutative color Hom-Leibniz-Poisson algebras and presente several constructions. Moreover we give the relationship between Hom-dialgebras and Hom-Leibniz-Poisson algebras; i.e. a Hom-dialgebras give rise to a Hom-Leibniz-Poisson algebra. Finally we show that twisting a color Hom-Leibniz module structure map by a color Hom-Leibniz algebra endomorphism, we get another one.

math.RA↗