| Title | Quasi-bom-Lie algebras, central extensions and 2-cocycle-like identities |
| Authors | Daniel Larsson, Sergei Silvestrov |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Algebra |
| Year | 2005 |
| Volume | 288 |
| Issue | 2 |
| Pages | 321 - 344 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Abstract English | 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 sigma-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 delta of derivations on the Laurent polynomials Ct,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. |
| Keywords | Loop algebras, Witt algebras, algebras, (color) Lie, quasi-hom-Lie algebras, deformations, central extensions, Virasoro algebras, |
| ISBN/ISSN/Other | ISSN: 0021-8693 |
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