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arXiv · 1503.06392

Representations and cohomologies of Hom-Lie-Yamaguti algebras with applications

Tao Zhang
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Abstract

The representation and cohomology theory of Hom-Lie-Yamaguti algebras is introduced. As an application, we study deformation and extension of Hom-Lie-Yamaguti algebras. It proved that a 1-parameter infinitesimal deformation of a Hom-Lie-Yamaguti algebra $T$ corresponds to a Hom-Lie-Yamaguti algebra of deformation type and a (2,3)-cocycle of $T$ with coefficients in the adjoint representation. We also prove that abelian extensions of Hom-Lie-Yamaguti algebras are classified by the (2,3)-cohomology group.

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Tao Zhang. 2015-04-06. Representations and cohomologies of Hom-Lie-Yamaguti algebras with applications. https://doi.org/10.4064/cm6903-6-2016

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