Principal Actions of Stacky Lie Groupoids

Author:

Bursztyn Henrique1,Noseda Francesco2,Zhu Chenchang3

Affiliation:

1. Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, Rio de Janeiro, Brazil

2. Instituto de Matemática - Universidade Federal do Rio de Janeiro, Avenida Athos da Silveira Ramos (Centro de Tecnologia - Bloco C), Rio de Janeiro, Brazil

3. Mathematisches Institut - Universität Göttingen, Bunsenstrasse, Göttingen, Germany

Abstract

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.

Funder

German Research Foundation

Deutsche Forschungsgemeinschaft

University of Göttingen

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference56 articles.

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2. Higher Gauge Theory;Baez,2007

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4. Geometric higher groupoids and categories;Behrend,2017

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1. Basic constructions over C∞-schemes;Journal of Geometry and Physics;2023-08

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