|
چکیده
|
In this paper, we introduce the class of split regular Hom-Leibniz–Poisson color algebras as the natural generalization of split regular Hom-Leibniz algebras, split regular Hom-Poisson algebras and split regular Hom-Leibniz–Poisson superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Leibniz–Poisson color algebra L is of the form L=U⊕∑[α]∈Π/∼I[α], with U a subspace of the abelian sub algebra H and any I[α], a well-described ideal of L, satisfying [I[α],I[β]]+μ(I[α],I[β])=0 if [α]≠[β]. Under certain conditions, in the case of L being of maximal length, the simplicity and the primeness of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split regular Hom-Leibniz–Poisson color algebra
|