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Representations of hom-Lie algebras. (English) Zbl 1294.17001
This paper provides a framework for the representation theory of hom-Lie algebras: the author defines the \(\alpha^k\)-derivation of a multiplicative hom-Lie algebra and considers the corresponding derivation extension; he defines the representation of a multiplicative hom-Lie algebra and the corresponding hom-cochain complexes and coboundary operators explicitly; he shows that central extensions of a multiplicative hom-Lie algebra are controlled by the second cohomology with coefficients in the trivial representation; he also studies the adjoint representations of a regular hom-Lie algebra; finally, he defines the hom-Nijenhuis operator of a regular hom-Lie algebra, which could give a trivial deformation.

17A30 Nonassociative algebras satisfying other identities
17B99 Lie algebras and Lie superalgebras
Full Text: DOI arXiv
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