On split Regular Hom-Leibniz algebras

Abstract

We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Leibniz algebra $L$ is of the form $L=U+\sum _{[j]\in \Lambda /\sim }{I}_{[j]}$ with $U$ a subspace of the abelian subalgebra $H$ and any $I_{[j]}$, a well described ideal of $L$, satisfying $[I_{[j]},I_{[k]}]=0$ if $[j]\ne [k]$. Under certain conditions, in the case of $L$ being of maximal length, the simplicity of the algebra is characterized.

arXiv admin note: substantial text overlap with arXiv:1411.7026

References in corpus (1)

• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras