# Poisson-Lie group

From Diffgeom

*This article or section of article is sourced from*:Wikipedia

## Contents

## Definition

A Poisson-Lie group is a differential manifold equipped with the following two additional structures:

- The structure of a Lie group
- The structure of a Poisson manifold (in other words, a Poisson algebra to the set )

satisfying the following compatibility conditions: the group multiplication is a Poisson map from with the Poisson product structure, to .