Some non-abelian phase spaces in low dimensions

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Bai, Chengming¹ 

[1] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

关键词: Lie algebra;    Phase space;    Para-Kahler structure;    Left-symmetric algebra;    S-equation;   

DOI  :  10.1016/j.geomphys.2008.08.001

来源: Elsevier

【 摘 要 】

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-Kahler 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. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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