Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493276 | Journal of Algebra | 2005 | 24 Pages |
Abstract
This paper introduces the notion of a quasi-hom-Lie algebra, or simply, a qhl-algebra, which is a natural generalization of hom-Lie algebras introduced in a previous paper [J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using Ï-derivations, math.QA/0408064]. Quasi-hom-Lie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by maps, twisting the Jacobi identity and skew-symmetry. The natural realm for these quasi-hom-Lie algebras is generalizations-deformations of the Witt algebra d of derivations on the Laurent polynomials C[t,tâ1]. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Daniel Larsson, Sergei D. Silvestrov,