Pseudo-euclidean Jordan algebras
| dc.creator | Baklouti, Amir | |
| dc.creator | Benayadi, Said | |
| dc.date | 2008-11-22 | |
| dc.date.accessioned | 2026-07-07T10:20:31Z | |
| dc.date.available | 2026-07-07T10:20:31Z | |
| dc.description | A Jordan algebra J is said to be pseudo-euclidean if J is endowed with an associative non-degenerate symmetric bilinear form B. B is said an associative scalar product on J. First, we provide a description of the pseudo-euclidean Jordan K-algebras in terms of double extensions and generalized double extensions. In particular, we shall use this description to construct all pseudo-euclidean Jordan algebras of dimension less than or equal to 5. And then, from one of these algebras, we shall construct a twelve dimension Lie algebra by the "TKK" construction. Second, a description of symplectic pseudo-euclidean Jordan algebras is provided and finally we describe a particular class of these algebras namely the class of symplectic Jordan-Manin Algebras. In addition to these descriptions, this paper demonstrates that these last two classes are identical and provides several information on the structure of pseudo-euclidean Jordan algebras. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/0811.3702 | |
| dc.identifier | http://arxiv.org/abs/0811.3702 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174874 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17C10, 17C20, 17C50, 17C55, 17B05, 17B62. | |
| dc.title | Pseudo-euclidean Jordan algebras | |
| dc.type | text |