Journal of Lie Theory 25 (2015), No. 3, 875--888
Copyright Heldermann Verlag 2015
Split Regular Hom-Lie Algebras
Maria Jesus Aragón Periñán
Dept. of Mathematics, University of Cádiz, 11510 Puerto Real -- Cádiz, Spain
mariajesus.aragonperin@alum.uca.es
Antonio Jesus Calderón Martín
Dept. of Mathematics, University of Cádiz, 11510 Puerto Real -- Cádiz
ajesus.calderon@uca.es
[Abstract-pdf]
\def\L{{\frak L}} We introduce the class of split regular Hom-Lie algebras as the natural extension of the one of split Lie algebras. We study its structure by showing that an arbitrary split regular Hom-Lie algebra ${\L}$ is of the form ${L}=U + \sum_{j}{I}_{j}$, where $U$ is a certain linear subspace of a maximal abelian subalgebra of ${\L}$ and the ${I}_{j}$ are well described (split) ideals of ${\L}$ satisfying $[{I}_j , {I}_k] = 0$ if $j\neq k$. Under certain conditions, the simplicity of ${\L}$ is characterized and it is shown that ${\L}$ is the direct sum of the family of its simple ideals.
Keywords: Hom-Lie algebra, roots, root space, structure theory.
MSC: 17A30, 17A60, 17B65, 17B22
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