The chiral WZNW phase space as a quasi-Poisson space

TL;DR

This paper demonstrates that the chiral WZNW phase space can be understood as a quasi-Poisson space linked to a Lie quasi-bialgebra, illustrating the concept of quasi-Poisson-Lie symmetry and enabling generalizations of dynamical twists.

Contribution

It establishes the chiral WZNW phase space as a quasi-Poisson space related to a classical limit of a Drinfeld quasi-Hopf algebra, connecting it to recent symmetry concepts.

Findings

Identifies the chiral WZNW phase space as a quasi-Poisson space.

Links the phase space to the classical limit of a Drinfeld quasi-Hopf algebra.

Enables generalization of dynamical twists in this context.

Abstract

It is explained that the chiral WZNW phase space is a quasi-Poisson space with respect to the `canonical' Lie quasi-bialgebra which is the classical limit of Drinfeld's quasi-Hopf deformation of the universal enveloping algebra. This exemplifies the notion of quasi-Poisson-Lie symmetry introduced recently by Alekseev and Kosmann-Schwarzbach, and also permits us to generalize certain dynamical twists considered previously in this example.