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On the Lie 2-algebra of sections of an LA-groupoid

Lookup NU author(s): Dr James Waldron

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Abstract

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.

Publication metadata

Author(s): Ortiz C, Waldron J

Publication type: Article

Publication status: Published

Journal: Journal of Geometry and Physics

Year: 2019

Volume: 145

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

Publisher: Elsevier

URL: https://doi.org/10.1016/j.geomphys.2019.07.005

DOI: 10.1016/j.geomphys.2019.07.005

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