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arXiv · 0808.1454

Some Non-Abelian Phase Spaces in Low Dimensions

Dongping Hou·Chengming Bai
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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 parakähler 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.

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Dongping Hou, Chengming Bai. 2008-08-11. Some Non-Abelian Phase Spaces in Low Dimensions. https://doi.org/10.1016/j.geomphys.2008.08.001

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