### Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras

(2007) In LUTFMA-5095-2007/1-16/(2007)- 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:
http://lup.lub.lu.se/record/959513

- author
- Makhlouf, Abdenacer and Silvestrov, Sergei
- 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
- 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
- id
- 1761ee50-b076-4ba5-b7b1-8256e166a5bd (old id 959513)
- alternative location
- http://arxiv.org/abs/0712.3130
- date added to LUP
- 2008-01-28 15:34:36
- date last changed
- 2016-04-16 06:21:31

@misc{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}, keyword = {cohomology,Hom-Poisson algebra,Deformation,Hom-associative algebra,Hom-Lie algebra}, language = {eng}, series = {LUTFMA-5095-2007/1-16/(2007)}, title = {Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras}, year = {2007}, }