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Quasi-bom-Lie algebras, central extensions and 2-cocycle-like identities

Larsson, Daniel LU and Silvestrov, Sergei LU (2005) In Journal of Algebra 288(2). p.321-344
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 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 C[t,t(-1)]. We also develop a theory of central extensions for qhl-algebras which can be used to deform and generalize... (More)
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 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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Loop algebras, Witt algebras, algebras, (color) Lie, quasi-hom-Lie algebras, deformations, central extensions, Virasoro algebras
in
Journal of Algebra
volume
288
issue
2
pages
321 - 344
publisher
Elsevier
external identifiers
  • wos:000229514700004
  • scopus:18744416558
ISSN
0021-8693
DOI
10.1016/j.jalgebra.2005.02.032
language
English
LU publication?
yes
id
66facc7f-51fb-4533-b2b5-02cd89df4f9a (old id 237454)
date added to LUP
2007-08-23 08:46:45
date last changed
2017-11-05 03:34:56
@article{66facc7f-51fb-4533-b2b5-02cd89df4f9a,
  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 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 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.},
  author       = {Larsson, Daniel and Silvestrov, Sergei},
  issn         = {0021-8693},
  keyword      = {Loop algebras,Witt algebras,algebras,(color) Lie,quasi-hom-Lie algebras,deformations,central extensions,Virasoro algebras},
  language     = {eng},
  number       = {2},
  pages        = {321--344},
  publisher    = {Elsevier},
  series       = {Journal of Algebra},
  title        = {Quasi-bom-Lie algebras, central extensions and 2-cocycle-like identities},
  url          = {http://dx.doi.org/10.1016/j.jalgebra.2005.02.032},
  volume       = {288},
  year         = {2005},
}