\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.
Maria Jesus Aragón Periñán
1
;
Antonio Jesus Calderón Martín
2
1
Dept. of Mathematics, University of Cádiz, 11510 Puerto Real -- Cádiz, Spain
2
Dept. of Mathematics, University of Cádiz, 11510 Puerto Real -- Cádiz
Maria Jesus Aragón Periñán; Antonio Jesus Calderón Martín. Split Regular Hom-Lie Algebras. Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 875-888. http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a11/
@article{JOLT_2015_25_3_a11,
author = {Maria Jesus Arag\'on Peri\~n\'an and Antonio Jesus Calder\'on Mart{\'\i}n},
title = {Split {Regular} {Hom-Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {875--888},
year = {2015},
volume = {25},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a11/}
}
TY - JOUR
AU - Maria Jesus Aragón Periñán
AU - Antonio Jesus Calderón Martín
TI - Split Regular Hom-Lie Algebras
JO - Journal of Lie Theory
PY - 2015
SP - 875
EP - 888
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a11/
ID - JOLT_2015_25_3_a11
ER -
%0 Journal Article
%A Maria Jesus Aragón Periñán
%A Antonio Jesus Calderón Martín
%T Split Regular Hom-Lie Algebras
%J Journal of Lie Theory
%D 2015
%P 875-888
%V 25
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a11/
%F JOLT_2015_25_3_a11
