Cohomologies, deformations and extensions of n-Hom-Lie algebras

JOURNAL OF GEOMETRY AND PHYSICS

卷:141

Article

Song, Lina¹  Tang, Rong¹ 

[1] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China

关键词: Dual representations;    Extensions;    Deformations;    Derivations;    Cohomologies;    n-Hom-Lie algebras;   

DOI  :  10.1016/j.geomphys.2019.03.003

来源: Elsevier

【 摘 要 】

In this paper, first we give the cohomologies of an n-Hom-Lie algebra and introduce the notion of a derivation of an n-Hom-Lie algebra. We show that a derivation of an n-Horn-Lie algebra is a 1-cocycle with the coefficient in the adjoint representation. We also give the formula of the dual representation of a representation of an n-Horn-Lie algebra. Then, we study (n-1)-order deformation of an n-Horri-Lie algebra. We introduce the notion of a Hom-Nijenhuis operator, which could generate a trivial (n-1)-order deformation of an n-Horn-Lie algebra. Finally, we introduce the notion of a generalized derivation of an n-Horn-Lie algebra, by which we can construct a new n-Horn-Lie algebra, which is called the generalized derivation extension of an n-Hom-Lie algebra. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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