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Irreducible Lie-Yamaguti algebras
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.Comment: 25 page
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