| Title | On some almost quadratic algebras coming from twisted derivations |
| Authors | Daniel Larsson, Gunnar Sigurdsson, Sergei Silvestrov |
| Alternative Location | http://dx.doi.org/10.2991/j... |
| Publication | Journal of Nonlinear Mathematical Physics |
| Year | 2006 |
| Volume | 13 |
| Pages | 76 - 86 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Atlantis Press |
| Abstract English | This paper explores the quasi-deformation scheme devised in 1, 3 as applied to the simple Lie algebra sl(2)(F) for specific choices of the involved parameters and underlying algebras. One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when the quasi-deformation method is applied to sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(F) is quasi-deformed into three-dimensional and four-dimensional Lie algebras and algebras closely resembling Lie superalgebras and colour Lie algebras, this being in stark contrast to the classical deformation schemes where sl(2)(F) is rigid. |
| Keywords | twisted Jacobi, extensions, sigma-derivations, quasi-deformation, colour Lie algebras, quasi-hom-Lie algebras, hom-Lie algebras, identities, almost quadratic algebras., |
| ISBN/ISSN/Other | ISSN: 1402-9251 |
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