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Deformations of Lie Algebras using σ-Derivations

Hartwig, Jonas ; Larsson, Daniel LU and Silvestrov, Sergei LU (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:
author
; and
organization
publishing date
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
Academic Press
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
2025-10-14 11:58:31
@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    = {{Academic Press}},
  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}},
}