Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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
and
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
2016-04-01 10:45:23
date last changed
2022-04-20 05:51:57
@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}},
  doi          = {{10.1515/FORUM.2010.040}},
  volume       = {{22}},
  year         = {{2010}},
}