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

Autor(es)

Ortiz, C. ^[1] ; Waldron, J. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo - Brazil

^[2] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne NE1 7RU, Tyne & Wear - England

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRY AND PHYSICS; v. 145, NOV 2019.
• Citações Web of Science: 0

Resumo

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. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 16/01630-6 - Estruturas geométricas generalizadas em geometria de Poisson equivariante
• Beneficiário: Cristián Andrés Ortiz González
• Modalidade de apoio: Auxílio à Pesquisa - Regular