A twisted generalization of Lie-Yamaguti algebras

Abstract

A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize Hom-Lie triple systems (and susequently ternary Hom-Nambu algebras) and Hom-Lie algebras in the same way as Lie-Yamaguti algebras generalize Lie triple systems and Lie algebras. It is shown that the category of Hom-Lie-Yamaguti algebras is closed under twisting by self-morphisms. Constructions of Hom-Lie-Yamaguti algebras from classical Lie-Yamaguti algebras and Malcev algebras are given. It is observed that, when the ternary operation of a Hom-Lie-Yamaguti algebra expresses through its binary one in a specific way, then such a Hom-Lie-Yamaguti algebra is a Hom-Malcev algebra.

arXiv comment12 pages

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Cited by in corpus (5)

• One-parameter formal deformations of Hom-Lie-Yamaguti algebras
• Hom-Lie-Yamaguti structures on Hom-Leibniz algebras
• On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras
• Representations and deformations of Hom-Lie-Yamaguti superalgebras