On the integration of Poisson homogeneous spaces

TL;DR

This paper develops a reduction method for describing the symplectic groupoid of Poisson homogeneous spaces, extending existing techniques to cases where the subgroup is not necessarily complete, thereby broadening the applicability of the theory.

Contribution

It introduces a reduction procedure for symplectic groupoids of Poisson homogeneous spaces that works even when the subgroup is non complete, advancing the understanding of Poisson Lie group quotients.

Findings

Provides a new reduction method for symplectic groupoids

Applicable to non complete coisotropic subgroups

Extends the theory of Poisson homogeneous spaces

Abstract

We study a reduction procedure for describing the symplectic groupoid of a Poisson homogeneous space obtained by quotient of a coisotropic subgroup. We perform it as a reduction of the Lu-Weinstein symplectic groupoid integrating Poisson Lie groups, that is suitable even for the non complete case.