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arXiv · 1508.02124

On split regular Hom-Lie color algebras

Yan Cao·Liangyun Chen
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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 $L = U + \sum\limits_{[j] \in \Lambda/\sim}I_{[j]}$ 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 $[j]\neq [k]$. Under certain conditions, in the case of $L$ being of maximal length, the simplicity of the algebra is characterized.

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Yan Cao, Liangyun Chen. 2015-08-10. On split regular Hom-Lie color algebras. https://arxiv.org/abs/1508.02124

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