Quasi-Hamiltonian groupoids and multiplicative Manin pairs

TL;DR

This paper reformulates quasi-Poisson structures using graded Poisson geometry, proves their integration into quasi-Hamiltonian groupoids, and connects these concepts with Dirac morphisms and Manin pairs for broader generalizations.

Contribution

It introduces a new formulation of quasi-Poisson structures in graded Poisson terms and establishes their integration into quasi-Hamiltonian groupoids, linking different mathematical frameworks.

Findings

Quasi-Poisson g-manifolds integrate into quasi-Hamiltonian g-groupoids.

The work connects Dirac morphisms with multiplicative Manin pairs.

Provides a broader context for potential generalizations.

Abstract

We reformulate notions from the theory of quasi-Poisson g-manifolds in terms of graded Poisson geometry and graded Poisson-Lie groups and prove that quasi-Poisson g-manifolds integrate to quasi-Hamiltonian g-groupoids. We then interpret this result within the theory of Dirac morphisms and multiplicative Manin pairs, to connect our work with more traditional approaches, and also to put it into a wider context suggesting possible generalizations.