Representations of hom-Lie algebras

Abstract

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.

arXiv comment16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-1098

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Cited by in corpus (86)

• Hom-Lie 2-algebras
• BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
• Yetter-Drinfeld modules for Hom-bialgebras
• Hom-Lie algebroids
• Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids
• $\mathcal{O}$-Operators on Hom-Lie algebras
• Representations of Bihom-Lie algebras
• Purely Hom-Lie bialgebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• Representations and module-extensions of hom 3-Lie algebras
• Twisting Poisson algebras, coPoisson algebras and Quantization
• Cohomology and 1-parameter formal deformations of Hom-Lie triple systems
• Hom-Big Brackets: Theory and Applications
• On split regular Hom-Lie superalgebras
• Quadratic color Hom-Lie algebras
• One-parameter formal deformations of Hom-Lie-Yamaguti algebras
• Generalized Derivations of Hom-Lie Superalgebras
• BiHom-Lie colour algebras structures
• Multiplicative Hom-Lie superalgebra structures on infinite dimensional simple Lie superalgebras of vector fields
• Deformations and generalized derivations of Hom-Lie conformal algebras
• Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
• Generalized Derivations and Rota-Baxter Operators of $n$-ary Hom-Nambu Superalgebras
• Constructions and Cohomology of color Hom-Lie algebras
• Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras
• Cohomology and deformations of compatible Hom-Lie algebras
• Another approach to Hom-Lie bialgebras via Manin triples
• Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras
• Quadratic $n$-ary Hom-Nambu algebras
• Second Cohomology of q-deformed Witt superalgebras
• Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras
• Deformation of Hom-Lie-Rinehart algebras
• Non-degenerate Killing forms on Hom-Lie superalgebras
• On Hom-Lie antialgebra
• Twisted O-operators on 3-Lie algebras and 3-NS-Lie algebras
• Cohomology and linear deformation of BiHom-left-symmetric algebras
• A complement on representations of Hom-Lie algebras
• Left counital Hopf algebra structures on free commutative Nijenhuis algebras
• Crossed modules for Hom-Lie antialgebras
• On split regular Hom-Leibniz-Rinehart algebras
• Chomology of Heisenberg Hom-Lie algebras
• Extensions of hom-Lie color algebras
• On the cohomology and extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras
• A non-abelian Hom-Leibniz tensor product and applications
• The constructions of 3-Hom-Lie bialgebras
• Biderivations and commuting linear maps on Hom-Lie algebras
• Sweedler duality for Hom-(co)algebras and Hom-(co)modules
• On 3-Hom-Lie-Rinehart algebras
• On some properties preserved by the non-abelian tensor product of Hom-Lie algebras
• Ado theorem for nilpotent Hom-Lie algebras
• Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields
• A non-abelian tensor product of Hom-Lie algebras
• Hom-Tensor Categories and the Hom-Yang-Baxter Equation
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras
• Cohomology and Versal Deformations of Hom-Leibniz algebras
• Equivalent description of Hom-Lie algebroids
• Matching Hom-Setting of Rota-Baxter algebras, dendriform algebras and pre-Lie algebras
• Cohomology characterizations of non-abelian extensions of Hom-Lie algebras
• Cohomologies, deformations and extensions of n-Hom-Lie algebras
• Four-angle Hopf modules for Hom-Hopf algebras
• Z-graded Hom-Lie Superalgebras
• Derivation Hom-Lie 2-algebras and non-abelian extensions of Hom-Lie algebras
• Generalized representations of 3-Hom-Lie algebras
• Classification of 3-Dimensional BiHom-Associative and BiHom-Bialgebras
• Hom-Lie algebra structures on quadratic Lie algebras and twisted invariant Killing-like forms defined on them
• Cohomology and Deformation of Virasoro Extensions of q-Witt Hom-Lie superalgebra
• A new approach to hom-Lie bialgebras
• Hom-pre-Malcev and Hom-M-Dendriform algebras
• Restricted hom-Lie algebras
• Enveloping algebras of color hom-Lie algebras
• Weighted $\mathcal{O}$-operators on Hom-Lie triple systems
• On hom-Lie algebras
• Algebras of quotients of Hom-Lie algebras
• Representations and $T$*-extensions of hom-Jordan-Lie algebras
• On the deformations and derivations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras
• The higher-order hom-associative Weyl algebras
• Representation up to homotopy of Hom-Lie algebroids
• Representations and deformations of Hom-Lie-Yamaguti superalgebras
• On the capablility of Hom-Lie algebras
• Hom-Nijienhuis operator and $T$*-extension of Hom-Lie Superalgebras
• Hom-Lie-Hopf algebras
• Structure of multiplicative simple Hom-Jordan algebras
• Universal central extensions of Hom-Lie antialgebras
• Hom-Lie groups of a class of Hom-Lie algebra
• (Bi)Hom-Leibniz algebras
• On BiHom-analogue of generalized Lie algebras
• $n$-ary Hom-Nambu algebras