The structure of split regular BiHom-Lie algebras

We introduce the class of split regular BiHom-Lie algebras as the natural extension of the one of split Hom-Lie algebras and so of split Lie algebras. We show that an arbitrary split regular BiHom-Lie algebra L is of the form L=U+∑jIj with U a linear subspace of a fixed maximal abelian subalgebra H...

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Bibliographic Details
Published in:Journal of geometry and physics 2016-12, Vol.110, p.296-305
Main Authors: Calderón, Antonio J., Sánchez, José M.
Format: Article
Language:English
Subjects:
BiHom-Lie algebra
Hom-Lie algebra
Lie algebra
Root
Root space
Structure theory
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Summary:We introduce the class of split regular BiHom-Lie algebras as the natural extension of the one of split Hom-Lie algebras and so of split Lie algebras. We show that an arbitrary split regular BiHom-Lie algebra L is of the form L=U+∑jIj with U a linear subspace of a fixed maximal abelian subalgebra H and any Ij a well described (split) ideal of L, satisfying [Ij,Ik]=0 if j≠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.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2016.08.004