Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 25 (2015), No. 3, 875--888Copyright 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 [ Fulltext-pdf  (293  KB)] for subscribers only.