Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1895126 | Journal of Geometry and Physics | 2008 | 10 Pages |
Abstract
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 para-Kähler 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Dongping Hou, Chengming Bai,