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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 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:
author
and
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 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}},
}