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Dirac Structures and Poisson Homogeneous Spaces

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Abstract:

Poisson homogeneous spaces for Poisson groupoids are classified in terms of Dirac structures for the corresponding Lie bialgebroids. Applications include Drinfel'd's classification in the case of Poisson groups and a description of leaf spaces of foliations as homogeneous spaces of pair groupoids.

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Authors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, 100871, China.¶E-mail: liuzj@sxx0.math.pku.edu.cn, , , , , , CN

    Zhang-Ju Liu

  2. Department of Mathematics, University of California, Berkeley, CA 94720, USA.¶E-mail: alanw@math.berkeley.edu, , , , , , US

    Alan Weinstein

  3. Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.¶E-mail: ping@math.psu.edu, , , , , , US

    Ping Xu

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  1. Zhang-Ju Liu
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  2. Alan Weinstein
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  3. Ping Xu
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Received: 31 December 1996 / Accepted: 20 June 1997

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Liu, ZJ., Weinstein, A. & Xu, P. Dirac Structures and Poisson Homogeneous Spaces . Comm Math Phys 192, 121–144 (1998). https://doi.org/10.1007/s002200050293

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  • DOI: https://doi.org/10.1007/s002200050293

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