Journal of Lie Theory

no. 3
Split Regular Hom-Lie Algebras
Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 875-888
\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.
DOI: 10.5802/jolt.864
Classification: 17A30, 17A60, 17B65, 17B22
Keywords: Hom-Lie algebra, roots, root space, structure theory 
@article{JOLT_2015_25_3_a11,
     author = {M. J. Arag\'on Peri\~n\'an and A. J. 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},
     doi = {10.5802/jolt.864},
     zbl = {1359.17042},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.864/}
}
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M. J. Aragón Periñán; A. J. Calderón Martín. Split Regular Hom-Lie Algebras. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 875-888. doi: 10.5802/jolt.864

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