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LOCAL FORMULAS FOR MULTIPLICATIVE FORMS

Transformation Groups volume 27, pages 371–401 (2022)Cite this article

Abstract

We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. In particular, we obtain local integrations and non-degenerate realizations of Poisson, Nijenhuis–Poisson, Dirac, and Jacobi structures by local symplectic, symplectic-Nijenhuis, presymplectic, and contact groupoids, respectively.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 21941-909, Brasil

    A. CABRERA

  2. Radboud University Nijmegen, IMAPP, 6500, GL, Nijmegen, The Netherlands

    I. MĂRCUŢ

  3. Instituto de Matemática e Estatística, GMA, Universidade Federal Fluminense, Rua Professor Marcos Waldemar de Freitas Reis s/n, Gragoatá Niterói, Rio de Janeiro, 24.210-201, Brasil

    M. A. SALAZAR

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  1. A. CABRERA
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  2. I. MĂRCUŢ
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  3. M. A. SALAZAR
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Correspondence to I. MĂRCUŢ.

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CABRERA, A., MĂRCUŢ, I. & SALAZAR, M.A. LOCAL FORMULAS FOR MULTIPLICATIVE FORMS. Transformation Groups 27, 371–401 (2022). https://doi.org/10.1007/s00031-020-09607-y

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  • DOI: https://doi.org/10.1007/s00031-020-09607-y