Multisymplectic geometry and Lie groupoids

TL;DR

This paper explores the generalization of symplectic groupoids to multisymplectic groupoids and investigates their infinitesimal counterparts, extending the classical Poisson structure framework.

Contribution

It introduces the concept of multisymplectic groupoids and identifies their infinitesimal structures, broadening the understanding of geometric structures related to Poisson geometry.

Findings

Basic examples of multisymplectic groupoids are provided

Infinitesimal counterparts of multisymplectic groupoids are characterized

Connections between higher-degree structures and classical Poisson structures are discussed

Abstract

We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe "higher'' versions of Poisson structures by identifying the infinitesimal counterparts of multisymplectic groupoids. Some basic examples and features are discussed.