%0 Journal Article
%T Irreducible Lie-Yamaguti algebras of Generic Type
%A Pilar Benito
%A Alberto Elduque
%A Fabian Martin-Herce
%J Mathematics
%D 2009
%I arXiv
%X 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 inner derivation algebras are the algebraic counterpart of the isotropy irreducible homogeneous spaces. These systems splits into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types were classified in a previous paper through a generalized Tits Construction of Lie algebras. In this paper, the Lie-Yamaguti algebras of generic type are classified by relating them to several other nonassociative algebraic systems: Lie and Jordan algebras and triple systems, Jordan pairs or Freudenthal triple systems.
%U http://arxiv.org/abs/0907.3622v1