Irreducible Lie-Yamaguti algebras of Generic Type
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Abstract
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.Keywords
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This publication has 24 references indexed in Scilit:
- New simple Lie superalgebras in characteristic 3Journal of Algebra, 2006
- SIMPLE $(-1,-1)$ BALANCED FREUDENTHAL KANTOR TRIPLE SYSTEMSGlasgow Mathematical Journal, 2003
- On triality and automorphisms and derivations of composition algebrasLinear Algebra and its Applications, 2000
- Lie algebras graded by finite root systems and intersection matrix algebrasInventiones Mathematicae, 1996
- The reductive pair (B3, G2) and affine connections on S7Journal of Pure and Applied Algebra, 1993
- Identity classification in triple systemsJournal of Algebra, 1985
- Dynkin diagrams for Lie triple systemsJournal of Algebra, 1980
- Introduction to Lie Algebras and Representation Theory1972
- On the structure of symplectic ternary algebrasIndagationes Mathematicae, 1972
- The geometry and structure of isotropy irreducible homogeneous spacesActa Mathematica, 1968