On Hom–Lie algebras

2015/02/18 by Yunhe Sheng, Zhen Xiong · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.1080/03081087.2015.1010473

Abstract

In this paper, first we show that is a Hom–Lie algebra if and only if is an differential graded-commutative algebra. Then, we revisit representations of Hom–Lie algebras and show that there are a series of coboundary operators. We also introduce the notion of an omni-Hom–Lie algebra associated to a vector space and an invertible linear map. We show that regular Hom–Lie algebra structures on a vector space can be characterized by Dirac structures in the corresponding omni-Hom–Lie algebra. The underlying algebraic structure of the omni-Hom–Lie algebra is a Hom–Leibniz algebra, or a Hom–Lie 2-algebra.

Cited by

• BiHom-Lie brackets and the Toda equation
• Equivalent description of Hom-Lie algebroids
• A non-abelian exterior product of Hom-Leibniz algebras

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