On split regular Hom-Lie color algebras
Volume 146 / 2017
Colloquium Mathematicum 146 (2017), 143-155
MSC: 17B75, 17A60, 17B22, 17B65.
DOI: 10.4064/cm6769-12-2015
Published online: 23 September 2016
Abstract
We introduce the class of split regular Hom-Lie color algebras as a natural generalization of split Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that every split regular Hom-Lie color algebra $L$ is of the form $L = U + \sum _{[j] \in \varLambda /\!\sim }I_{[j]}$ with $U$ a subspace of an abelian graded subalgebra $H$ and any $I_{[j]}$ a well-described ideal of $L$, satisfying $[I_{[j]}, I_{[k]}] = 0$ if $[j]\not =[k]$. Under certain conditions, in the case of $L$ being of maximal length, the simplicity of the algebra is characterized.
