Quotients of multiplicative forms and Poisson reduction

TL;DR

This paper investigates how differential forms on Lie algebroids and groupoids behave under quotients, leading to generalized reduction methods for Poisson and Dirac structures, and unifying existing results.

Contribution

It provides Lie theoretic conditions for basic forms on quotients and characterizes the induced forms, extending Poisson reduction theory.

Findings

Identified conditions for forms to be basic on quotients

Characterized induced forms on quotient structures

Unified various Poisson reduction results

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.