Some Non-Abelian Phase Spaces in Low Dimensions
| Autor: | Hou, Dongping, Bai, Chengming |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Journal of Geometry and Physics 58 (2008) 1752-1761 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.geomphys.2008.08.001 |
| Popis: | A non-abelian phase space, or a phase space of a Lie algebra is a generalization of the usual (abelian) phase space of a vector space. It corresponds to a parak\"ahler structure in geometry. Its structure can be interpreted in terms of left-symmetric algebras. In particular, a solution of an algebraic equation in a left-symmetric algebra which is an analogue of classical Yang-Baxter equation in a Lie algebra can induce a phase space. In this paper, we find that such phase spaces have a symplectically isomorphic property. We also give all such phase spaces in dimension 4 and some examples in dimension 6. These examples can be a guide for a further development. Comment: 16 pages, appear in Journal of Geometry and Physics |
| Databáze: | arXiv |
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