Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
(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:
https://lup.lub.lu.se/record/1657963
- author
- Makhlouf, Abdenacer and Silvestrov, Sergei LU
- organization
- publishing date
- 2010
- 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}}, }