| Title | Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras |
| Authors | Abdenacer Makhlouf, Sergei Silvestrov |
| Alternative Location | http://dx.doi.org/10.1515/F..., Restricted Access |
| Publication | Forum Mathematicum |
| Year | 2010 |
| Volume | 22 |
| Issue | 4 |
| Pages | 715 - 739 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Walter de Gruyter & Co |
| Abstract English | 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 sl(2)(K) and describe as formal deformations the q-deformed Witt algebra and Jackson sl(2)(K). |
| ISBN/ISSN/Other | ISSN: 0933-7741 |
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