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Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities. (English) Zbl 1099.17015
The authors first introduce the notion of quasi-hom-Lie algebras, a natural generalization of hom-Lie algebras introduced by J. T. Hartwig and the authors [J. Algebra 295, No. 2, 314–361 (2006; Zbl 1138.17012)]. Quasi-hom-Lie algebras include color Lie algebras and superalgebras, and can be seen as deformations of these by maps, twisting the Jacobi identity and skew-symmetry. The goal for introducing the quasi-hom-Lie algebras is to generalize or deform the Witt algebra of derivations on the Laurent polynomials $${\mathbb C}[t,t^{-1}]$$. A theory of central extensions for quasi-hom-Lie algebras is developed. The main result of the paper is the description of central extensions of quasi-hom-Lie algebras in terms of equivalence classes of 2-cocycle-like maps.
Reviewer: Yucai Su (Hefei)

##### MSC:
 17B61 Hom-Lie and related algebras 17B56 Cohomology of Lie (super)algebras 17B68 Virasoro and related algebras
##### Keywords:
Quasi-hom-Lie algebras; central extensions; deformations
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