On Split Regular Hom-Poisson Color Algebras

摘要

We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras.By developing techniques of connections of roots for this kind of algebras,we show that such a split regular Hom-Poisson color algebras A is of the form A =U + ∑α Iα with U a subspace of a maximal abelian subalgebra H and any Iα,a well described ideal of A,satisfying [Iα,Iβ] + IαIβ =0 if [α] ≠ [β].Under certain conditions,in the case of A being of maximal length,the simplicity of the algebra is characterized.