Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
(2007) In Preprints in Mathematical Sciences- Abstract
- The aim of this paper is to extend to Hom-algebra structures the theory of formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and extended to Lie algebras by Nijenhuis-Richardson. We deal with Hom-associative and Hom-Lie algebras. We construct the first groups of a deformation cohomology and give several examples of deformations. We provide families of Hom-Lie algebras deforming Lie algebra sl2 and describe as formal deformations the
q-deformed Witt algebra and Jackson sl2.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/959513
- author
- Makhlouf, Abdenacer and Silvestrov, Sergei LU
- organization
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- submitted
- subject
- keywords
- cohomology, Hom-Poisson algebra, Deformation, Hom-associative algebra, Hom-Lie algebra
- in
- Preprints in Mathematical Sciences
- publisher
- Lund University
- external identifiers
-
- other:LUTFMA-5095-2007/1-16/(2007)
- ISSN
- 1403-9338
- project
- Non-commutative Analysis of Dynamics, Fractals and Wavelets
- Non-commutative Geometry in Mathematics and Physics
- language
- English
- LU publication?
- yes
- additional info
- submitted on 19 dec 2007
- id
- 1761ee50-b076-4ba5-b7b1-8256e166a5bd (old id 959513)
- alternative location
- http://arxiv.org/abs/0712.3130
- date added to LUP
- 2016-04-04 09:12:00
- date last changed
- 2018-11-21 20:51:26
@article{1761ee50-b076-4ba5-b7b1-8256e166a5bd, abstract = {{The aim of this paper is to extend to Hom-algebra structures the theory of formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and extended to Lie algebras by Nijenhuis-Richardson. We deal with Hom-associative and Hom-Lie algebras. We construct the first groups of a deformation cohomology and give several examples of deformations. We provide families of Hom-Lie algebras deforming Lie algebra sl2 and describe as formal deformations the <br/><br> q-deformed Witt algebra and Jackson sl2.}}, author = {{Makhlouf, Abdenacer and Silvestrov, Sergei}}, issn = {{1403-9338}}, keywords = {{cohomology; Hom-Poisson algebra; Deformation; Hom-associative algebra; Hom-Lie algebra}}, language = {{eng}}, publisher = {{Lund University}}, series = {{Preprints in Mathematical Sciences}}, title = {{Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras}}, url = {{http://arxiv.org/abs/0712.3130}}, year = {{2007}}, }