Principal actions of stacky Lie groupoids

2015/10/30 by Henrique Bursztyn, Bursztyn, Henrique, Francesco Noseda +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1510.09208

openalex publication_date 2015/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, i.e., 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.

Citations

• Topological and Smooth Stacks
• Integrating central extensions of Lie algebras via Lie 2-groups
• Notes on Grothendieck topologies, fibered categories and descent theory
• Poisson geometry and Morita equivalence
• Higher Groupoid Actions, Bibundles, and Differentiation

Cited by

• Hamiltonian actions on 0-shifted cosymplectic groupoids

Related

• Lie n-groupoids and stacky Lie groupoids
• Geometric structures on Lie groupoids and differentiable stacks
• On the cohomology of differentiable stacks
• Lie Groupoids
• Lie Algebroids over Differentiable Stacks