LOCAL FORMULAS FOR MULTIPLICATIVE FORMS

LOCAL FORMULAS FOR MULTIPLICATIVE FORMS

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 define...

Full description

Saved in:
Bibliographic Details
Published in:Transformation groups Vol. 27; no. 2; pp. 371 - 401
Main Authors: CABRERA, A., MĂRCUŢ, I., SALAZAR, M. A.
Format: Journal Article
Language:English
Published: New York Springer US 01-06-2022
Springer Nature B.V
Subjects:
Algebra
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-020-09607-y