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

Makhlouf, Abdenacer and Silvestrov, Sergei LU (2007) In Preprints in Mathematical Sciences1999-01-01+01:00
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:
author
organization
publishing date
type
Contribution to journal
publication status
submitted
subject
keywords
cohomology, Hom-Poisson algebra, Deformation, Hom-associative algebra, Hom-Lie algebra
in
Preprints in Mathematical Sciences1999-01-01+01:00
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
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
2016-11-25 14:39:43
@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},
  keyword      = {cohomology,Hom-Poisson algebra,Deformation,Hom-associative algebra,Hom-Lie algebra},
  language     = {eng},
  publisher    = {Lund University},
  series       = {Preprints in Mathematical Sciences1999-01-01+01:00},
  title        = {Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras},
  year         = {2007},
}