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Publication Date:
February 2010
ISSN:
1435-5337
DOI:
10.1515/forum.2010.040

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Forum Mathematicum

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Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras

Abdenacer Makhlouf1 / Sergei Silvestrov2

1Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4, rue des Frères Lumière F-68093 Mulhouse, France. Abdenacer.Makhlouf@uha.fr

2Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden. sergei.silvestrov@math.lth.se

Citation Information: Forum Mathematicum. Volume 22, Issue 4, Pages 715–739, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/forum.2010.040, February 2010

Publication History:
Received:
2007-12-24
Revised:
2008-09-03
Accepted:
2008-11-26
Published Online:
2010-02-08

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 𝔰𝔩2(𝕂) and describe as formal deformations the q-deformed Witt algebra and Jackson 𝔰𝔩2(𝕂).

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