The chiral WZNW phase space as a quasi-Poisson space

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.

arXiv comment11 pages, LaTeX, expanded by a new section in v2

References in corpus (5)

• The non-commutative Weil algebra
• Lattice Wess-Zumino-Witten Model and Quantum Groups
• Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids
• An explicit construction of the quantum group in chiral WZW-models
• Quasi-Poisson Manifolds

Cited by in corpus (5)

• Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
• Dynamical r-matrices and the chiral WZNW phase space
• The non-Abelian momentum map for Poisson-Lie symmetries on the chiral WZNW phase space
• Zero modes of the SU(2)_k Wess-Zumino-Novikov-Witten model in Euler angles parametrization
• Dynamical r-matrices and Poisson-Lie symmetries in the chiral WZNW model