Representations of Hom-Lie Algebras

By Y. Sheng. 2010

302 citations recorded by the source corpus.

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/df631308489477f5c6e2c6a016dc85d22f38f935

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras (2015, methodology): “The fact that ϕis unital is equivalent to ϕ(1A) = βM, which is equivalent to 1A· m= βM(m), for all m∈ M, which is equivalent to saying that the module Mis unital. We recall the following concept from [34] (see also [7] on this subject). Deﬁnition 3.5 ([34]) Let (L,[−],α) be a Hom-Lie algebra. A repr”
On universal central extensions of Hom-Lie algebras (2012, background): “From the introductory paper [9], this algebraic structure and other related ones as Hom-associative, Hom-Leibniz and Hom-Nambu algebras were studied in several papers [10, 13, 14, 15, 16, 17, 18, 19] and references given therein.”
Yetter-Drinfeld modules for Hom-bialgebras (2013, background): “For instance, representation theory, cohomology and deformation theory for Hom-associative algebras and Hom-Lie algebras have been developed in [2, 28, 31].”