Geodesic
Representations and cohomologies of Hom-Lie–Yamaguti algebras with applications
Tao Zhang 1   ; Juan Li 1
1 College of Mathematics and Information Science Henan Normal University Xinxiang 453007, P.R. China
Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 131-155 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The representation and cohomology theory of Hom-Lie–Yamaguti algebras are introduced. As an application, we study deformation and extension of Hom-Lie–Yamaguti algebras. It is 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.
DOI : 10.4064/cm6903-6-2016
Keywords: representation cohomology theory hom lie yamaguti algebras introduced application study deformation extension hom lie yamaguti algebras proved parameter infinitesimal deformation hom lie yamaguti algebra corresponds hom lie yamaguti algebra deformation type cocycle coefficients adjoint representation prove abelian extensions hom lie yamaguti algebras classified cohomology group

Tao Zhang  1   ; Juan Li  1

1 College of Mathematics and Information Science Henan Normal University Xinxiang 453007, P.R. China 
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Tao Zhang; Juan Li. Representations and cohomologies of Hom-Lie–Yamaguti algebras with applications. Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 131-155. doi: 10.4064/cm6903-6-2016

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