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Quasi-Deformations of sl2(F) Using Twisted Derivations

Silvestrov, Sergei LU and Larsson, Daniel LU (2007) In Communications in Algebra 35(12). p.4303-4318
Abstract
In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) to the simple 3-dimensional Lie algebra sl2(F). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to sl2(F) we can, by choosing parameters suitably, deform sl2(F) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where sl2(F) is rigid.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Twisted derivation, Quasi-deformations, Twisted Jacobi identity, Quasi-Lie algebras
in
Communications in Algebra
volume
35
issue
12
pages
4303 - 4318
publisher
Taylor & Francis
external identifiers
  • wos:000251875700039
  • scopus:37249062267
ISSN
0092-7872
DOI
10.1080/00927870701545127
project
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
language
English
LU publication?
yes
id
90c5d4ef-2873-43c7-b006-d6bbfeed3984 (old id 939447)
alternative location
http://www.informaworld.com/smpp/content~content=a788544216~db=all~order=page
date added to LUP
2008-01-22 13:49:26
date last changed
2017-08-13 03:33:49
@article{90c5d4ef-2873-43c7-b006-d6bbfeed3984,
  abstract     = {In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) to the simple 3-dimensional Lie algebra sl2(F). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to sl2(F) we can, by choosing parameters suitably, deform sl2(F) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where sl2(F) is rigid.},
  author       = {Silvestrov, Sergei and Larsson, Daniel},
  issn         = {0092-7872},
  keyword      = {Twisted derivation,Quasi-deformations,Twisted Jacobi identity,Quasi-Lie algebras},
  language     = {eng},
  number       = {12},
  pages        = {4303--4318},
  publisher    = {Taylor & Francis},
  series       = {Communications in Algebra},
  title        = {Quasi-Deformations of sl2(F) Using Twisted Derivations},
  url          = {http://dx.doi.org/10.1080/00927870701545127},
  volume       = {35},
  year         = {2007},
}