Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Volume 2020, Issue 16, Pages 5055-5125Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rny142
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Funding
- Research Foundation of the State of Rio de Janeiro (Faperj)
- Brazilian National Council for Scientific and Technological Development (CNPq)
- German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Gottingen
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Stacky Lie groupoids are generalizations of Lie groupoids in which the space of arrows of the groupoid is a differentiable stack. In this paper, we consider actions of stacky Lie groupoids on differentiable stacks and their associated quotients. We provide a characterization of principal actions of stacky Lie groupoids, that is, actions whose quotients are again differentiable stacks in such a way that the projection onto the quotient is a principal bundle. As an application, we extend the notion of Morita equivalence of Lie groupoids to the realm of stacky Lie groupoids, providing examples that naturally arise from non-integrable Lie algebroids.
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