Quasi-bom-Lie algebras, central extensions and 2-cocycle-like identities
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/237454
- author
- Larsson, Daniel LU and Silvestrov, Sergei LU
- organization
- publishing date
- 2005
- 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
- 2016-04-01 11:54:53
- date last changed
- 2022-03-28 17:33:47
@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}}, keywords = {{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}}, doi = {{10.1016/j.jalgebra.2005.02.032}}, volume = {{288}}, year = {{2005}}, }