| Title | Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras |
| Authors | Abdenacer Makhlouf, Sergei Silvestrov |
| Alternative Location | http://arxiv.org/abs/0712.3130 |
| Publication | LUTFMA-5095-2007/1-16/(2007) |
| Year | 2007 |
| Document type | Article |
| Status | Submitted |
| Language | eng |
| Abstract English | 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> q-deformed Witt algebra and Jackson sl2. |
| Keywords | cohomology, Hom-Poisson algebra, Deformation, Hom-associative algebra, Hom-Lie algebra, |
| ISBN/ISSN/Other | ISSN: 1403-9338 |
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