Representations and module-extensions of hom 3-Lie algebras

Abstract

In this paper, we study the representations and module-extensions of hom 3-Lie algebras. We show that a linear map between hom 3-Lie algebras is a morphism if and only if its graph is a hom 3-Lie subalgebra and show that the derivations of a hom 3-Lie algebra is a Lie algebra. Derivation extension of hom 3-Lie algebras are also studied as an application. Moreover, we introduce the definition of $T_{\theta }$-extensions and $T_{\theta }^{\ast }$-extensions of hom 3-Lie sub-algebras in terms of modules, provide the necessary and sufficient conditions for $2k$-dimensional metric hom 3-Lie algebra to be isomorphic to a $T_{\theta }^{\ast }$-extensions.

arXiv admin note: substantial text overlap with arXiv:1005.0140 by other authors

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Cited by in corpus (9)

• Representations of Bihom-Lie algebras
• Split Regular $Hom$-Leibniz Color $3$-Algebras
• Local cocycle 3-Hom-Lie Bialgebras and 3-Lie Classical Hom-Yang-Baxter Equation
• On 3-Hom-Lie-Rinehart algebras
• Constructions and $T^{\ast }$-Extensions of 3-Bihom-Lie Superalgebras
• Quadratic and symplectic structures on 3-(Hom)-$\rho$-Lie algebras
• The constructions of 3-Hom-Lie bialgebras
• The construction of 3-Bihom-Lie algebras
• Cohomologies, deformations and extensions of n-Hom-Lie algebras