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Vector fields and derivations on differentiable stacks

Lookup NU author(s): Dr James Waldron

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Abstract

We introduce and study module structures on both the dgla of multiplicative vector fields and the graded algebra of functions on Lie groupoids. We show that there is an associated structure of a graded Lie-Rinehart algebra on the vector fields of a differentiable stack over its smooth functions that is Morita invariant in an appropriate sense. Furthermore, we show that associated Van-Est type maps are compatible with those module structures. We also present several examples.

Publication metadata

Author(s): Herrera-Carmona JS, Ortiz C, Waldron J

Publication type: Article

Publication status: Published

Journal: Differential Geometry and its Applications

Year: 2025

Volume: 101

Print publication date: 01/12/2025

Online publication date: 16/09/2025

Acceptance date: 03/09/2025

Date deposited: 07/01/2026

ISSN (print): 0926-2245

ISSN (electronic): 1872-6984

Publisher: Elsevier

URL: https://doi.org/10.1016/j.difgeo.2025.102292

DOI: 10.1016/j.difgeo.2025.102292

ePrints DOI: 10.57711/taf5-t585

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