Deformations of Lie Algebras using σ-Derivations
(2006) In Journal of Algebra 295(2). p.314-361- Abstract
- In this article we develop an approach to deformations of the Witt and Virasoro algebras based on sigma-derivations. We show that sigma-twisted Jacobi type identity holds for generators of such deformations. For the sigma-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie algebras and their central extensions, which in particular include naturally the q-deformations of the Witt and Virasoro algebras associated to q-difference operators, providing also corresponding q-deformed Jacobi identities. (c) 2005 Elsevier Inc. All rights reserved.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/421328
- author
- Hartwig, Jonas ; Larsson, Daniel LU and Silvestrov, Sergei LU
- organization
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- q-Witt algebras, q-Virasoro algebras, Jacobi, type identities, Lie algebras, sigma-derivations, extensions, deformation theory
- in
- Journal of Algebra
- volume
- 295
- issue
- 2
- pages
- 314 - 361
- publisher
- Elsevier
- external identifiers
-
- wos:000234518100002
- scopus:31044436281
- ISSN
- 0021-8693
- DOI
- 10.1016/j.jalgebra.2005.07.036
- language
- English
- LU publication?
- yes
- id
- de6109b3-2340-4347-bed3-6f15455c23e2 (old id 421328)
- date added to LUP
- 2016-04-01 11:46:51
- date last changed
- 2022-04-20 21:36:10
@article{de6109b3-2340-4347-bed3-6f15455c23e2, abstract = {{In this article we develop an approach to deformations of the Witt and Virasoro algebras based on sigma-derivations. We show that sigma-twisted Jacobi type identity holds for generators of such deformations. For the sigma-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie algebras and their central extensions, which in particular include naturally the q-deformations of the Witt and Virasoro algebras associated to q-difference operators, providing also corresponding q-deformed Jacobi identities. (c) 2005 Elsevier Inc. All rights reserved.}}, author = {{Hartwig, Jonas and Larsson, Daniel and Silvestrov, Sergei}}, issn = {{0021-8693}}, keywords = {{q-Witt algebras; q-Virasoro algebras; Jacobi; type identities; Lie algebras; sigma-derivations; extensions; deformation theory}}, language = {{eng}}, number = {{2}}, pages = {{314--361}}, publisher = {{Elsevier}}, series = {{Journal of Algebra}}, title = {{Deformations of Lie Algebras using σ-Derivations}}, url = {{http://dx.doi.org/10.1016/j.jalgebra.2005.07.036}}, doi = {{10.1016/j.jalgebra.2005.07.036}}, volume = {{295}}, year = {{2006}}, }