Quotients of multiplicative forms and Poisson reduction
Differential Geometry
2023-01-02 v1 Symplectic Geometry
Abstract
In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify Lie theoretic conditions under which such forms become basic and characterize the induced forms on the quotients. We apply these results to describe generalized quotient and reduction processes for (twisted) Poisson and Dirac structures, as well as to their integration by (twisted, pre-)symplectic groupoids. In particular, we recover and generalize several known results concerning Poisson reduction.
Cite
@article{arxiv.2008.03416,
title = {Quotients of multiplicative forms and Poisson reduction},
author = {Alejandro Cabrera and Cristian Ortiz},
journal= {arXiv preprint arXiv:2008.03416},
year = {2023}
}