Symmetries and reduction of multiplicative 2-forms

Henrique Bursztyn; Alejandro Cabrera

doi:10.3934/jgm.2012.4.111

Article Contents

2012, Volume 4, Issue 2: 111-127. Doi: 10.3934/jgm.2012.4.111

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Symmetries and reduction of multiplicative 2-forms

Henrique Bursztyn^1, and
Alejandro Cabrera^2,

1.
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320
2.
Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, CEP 21941-909, Rio de Janeiro - RJ

Received: February 28, 2011

Revised: June 30, 2011

Published: May 2012

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Abstract

This paper is concerned with symmetries of closed multiplicative 2-forms on Lie groupoids and their infinitesimal counterparts. We use them to study Lie group actions on Dirac manifolds by Dirac diffeomorphisms and their lifts to presymplectic groupoids, building on recent work of Fernandes-Ortega-Ratiu [11] on Poisson actions.

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Mathematics Subject Classification: Primary: 53D17.

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