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Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras

Makhlouf, Abdenacer and Silvestrov, Sergei LU (2010) In Forum Mathematicum 22(4). p.715-739
Abstract
The aim of this paper is to extend to Hom-algebra structures the theory of 1-parameter formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and extended to Lie algebras by Nijenhuis and Richardson. In this paper, formal deformations of Hom-associative and Hom-Lie algebras are studied. The first groups of a deformation cohomology are constructed and several examples of deformations are given. We also provide families of Hom-Lie algebras deforming Lie algebra sl(2)(K) and describe as formal deformations the q-deformed Witt algebra and Jackson sl(2)(K).
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Forum Mathematicum
volume
22
issue
4
pages
715 - 739
publisher
De Gruyter
external identifiers
  • wos:000279640700008
  • scopus:77953349114
ISSN
1435-5337
DOI
10.1515/FORUM.2010.040
language
English
LU publication?
yes
id
be4dac12-5124-46e4-a72a-ee1498819d07 (old id 1657963)
date added to LUP
2010-08-20 09:47:37
date last changed
2018-07-15 03:16:44
@article{be4dac12-5124-46e4-a72a-ee1498819d07,
  abstract     = {The aim of this paper is to extend to Hom-algebra structures the theory of 1-parameter formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and extended to Lie algebras by Nijenhuis and Richardson. In this paper, formal deformations of Hom-associative and Hom-Lie algebras are studied. The first groups of a deformation cohomology are constructed and several examples of deformations are given. We also provide families of Hom-Lie algebras deforming Lie algebra sl(2)(K) and describe as formal deformations the q-deformed Witt algebra and Jackson sl(2)(K).},
  author       = {Makhlouf, Abdenacer and Silvestrov, Sergei},
  issn         = {1435-5337},
  language     = {eng},
  number       = {4},
  pages        = {715--739},
  publisher    = {De Gruyter},
  series       = {Forum Mathematicum},
  title        = {Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras},
  url          = {http://dx.doi.org/10.1515/FORUM.2010.040},
  volume       = {22},
  year         = {2010},
}