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Lookup NU author(s): Dr James Waldron
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).
In this work we introduce the category of multiplicative sections of an LA-groupoid. We prove that this category carries a natural strict Lie 2-algebra structure, which is Morita invariant. As applications, we study the algebraic structure underlying multiplicative vector fields on a Lie groupoid and in particular vector fields on differentiable stacks. We also introduce the notion of geometric vector field on the quotient stack of a Lie groupoid, showing that the space of such vector fields is a Lie algebra. We describe the Lie algebra of geometric vector fields in several cases, including classifying stacks, quotient stacks of regular Lie groupoids and in particular orbifolds, and foliation groupoids.
Author(s): Ortiz C, Waldron J
Publication type: Article
Publication status: Published
Journal: Journal of Geometry and Physics
Print publication date: 01/11/2019
Online publication date: 15/07/2019
Acceptance date: 06/07/2019
Date deposited: 10/10/2019
ISSN (electronic): 0393-0440
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