Quasi-hom-Lie Algebras, Central Extensions and 2-cocycle-like Identities

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dc.creatorLarsson, Daniel
dc.creatorSilvestrov, Sergei
dc.date2004-08-04
dc.date.accessioned2026-07-07T05:11:01Z
dc.date.available2026-07-07T05:11:01Z
dc.descriptionThis paper begins by introducing the concept of a quasi-hom-Lie algebra which is a natural generalization of hom-Lie algebras introduced in a previous paper by the authors. Quasi-hom-Lie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by homomorphisms, twisting the Jacobi identity and skew-symmetry. The natural realm for these quasi-hom-Lie algebras is as a generalization-deformation of the Witt algebra $\Witt$ of derivations on the Laurent polynomials $\C[t,t^{-1}]$. We also develop a theory of central extensions for qhl-algebras which can be used to deform and generalize the Virasoro algebra by centrally extending the deformed Witt type algebras constructed here. In addition, we give a number of other interesting examples of quasi-hom-Lie algebras, among them a deformation of the loop algebra.
dc.description40 pages
dc.identifierhttps://arxiv.org/abs/math/0408061
dc.identifierhttp://arxiv.org/abs/math/0408061
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72109
dc.subjectRings and Algebras
dc.subjectQuantum Algebra
dc.subject17B99 (Primary) 17B75, 17B68, 17A36, 17B40, 17B65, 17B66, 17B56 (Secondary)
dc.titleQuasi-hom-Lie Algebras, Central Extensions and 2-cocycle-like Identities
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