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arXiv · 1504.04236

On split Regular Hom-Leibniz algebras

Yan Cao·Liangyun Chen
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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 $L = U + \sum\limits_{[j] \in \Lambda/\sim}I_{[j]}$ 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 $[j]\neq [k]$. 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. 2015-04-16. On split Regular Hom-Leibniz algebras. https://doi.org/10.1142/s0219498818501852

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