On split regular Hom-Lie color algebras

Abstract

We introduce the class of split regular Hom-Lie color algebras as the natural generalization of split Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Lie color algebra $L$ is of the form $L=U+\sum _{[j]\in \Lambda /\sim }{I}_{[j]}$ with $U$ a subspace of the abelian graded 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.

13. arXiv admin note: substantial text overlap with arXiv:1504.04236

References in corpus (2)

• Deformations of Lie Algebras using $\sigma$-derivations
• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras