Coadjoint orbits of Lie groupoids

JOURNAL OF GEOMETRY AND PHYSICS

卷:129

Article

Liu, Zhangju¹ 

[1] China Agr Univ, Dept Appl Math, Beijing 100873, Peoples R China

关键词: Jet groupoids;    Coadjoint orbits;    Symplectic leaves;   

DOI  :  10.1016/j.geomphys.2018.03.011

来源: Elsevier

【 摘 要 】

For a Lie groupoid g with Lie algebroid A, we realize the symplectic leaves of the Lie-Poisson structure on A* as orbits of the affine coadjoint action of the Lie groupoid Jg * T*M on A*, which coincide with the groupoid orbits of the symplectic groupoid T*g over A*. It is also shown that there is a fiber bundle structure on each symplectic leaf. In the case of gauge groupoids, a symplectic leaf is the universal phase space for a classical particle in a Yang-Mills field. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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