Irreducible Lie-Yamaguti algebras

Details Irreducible Lie-Yamaguti algebras Irreducible Lie-Yamaguti algebras

2008-10-02

arxiv.org/abs/0810.0440v1

Mathematics

Rings and Algebras

25 pages

Scientific paper

Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules over their Lie inner derivation algebra are the algebraic counterpart of the isotropy irreducible homogeneous spaces. These systems will be shown to split into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types will be classified and most of them will be shown to be related to a Generalized Tits Construction of Lie algebras.

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