Principal Actions of Stacky Lie Groupoids
2018 ◽
Vol 2020
(16)
◽
pp. 5055-5125
Keyword(s):
Abstract 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.
2018 ◽
Vol 356
(4)
◽
pp. 376-381
◽
2020 ◽
Vol 2020
(760)
◽
pp. 267-293
◽
Keyword(s):
1987 ◽
pp. 82-184
◽
1988 ◽
Vol 19
(1)
◽
pp. 358-363
◽
Keyword(s):