Homogeneous spaces of Dirac groupoids

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• 作者：Madeleine Jotz Lean ^{M.Jotz-Lean@sheffield.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary 53D17 ; 70H45 ; secondary 22A22
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：104
• 期：Complete
• 页码：89-111
• 全文大小：529 K

文摘

A Poisson structure on a homogeneous space of a Poisson groupoid is homogeneous if the action of the Lie groupoid on the homogeneous space is compatible with the Poisson structures. According to a result of Liu, Weinstein and Xu, Poisson homogeneous spaces of a Poisson groupoid are in correspondence with suitable Dirac structures in the Courant algebroid defined by the Lie bialgebroid of the Poisson groupoid. We show that this correspondence result fits into a more natural context: the one of Dirac groupoids, which are objects generalizing Poisson groupoids and multiplicative closed 2-forms on groupoids.