
Journal of Lie Theory 25 (2015), No. 3, 875888 Copyright Heldermann Verlag 2015 Split Regular HomLie 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 [Abstractpdf] \def\L{{\frak L}} We introduce the class of split regular HomLie algebras as the natural extension of the one of split Lie algebras. We study its structure by showing that an arbitrary split regular HomLie 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: HomLie algebra, roots, root space, structure theory. MSC: 17A30, 17A60, 17B65, 17B22 [ Fulltextpdf (293 KB)] for subscribers only. 