A supergeometric approach to Poisson reduction

TL;DR

This paper presents a unified supergeometric framework for Poisson reduction, generalizing classical methods and enabling the construction of Lie 2-group actions within the same setting.

Contribution

It introduces a supergeometric approach to Poisson reduction that generalizes classical techniques and incorporates Lie 2-group actions.

Findings

Unified supergeometric framework for Poisson reduction

Generalization of Marsden-Ratiu reduction

Construction of strict Lie 2-group actions

Abstract

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to describe the corresponding reductions.