The Chiral WZNW Phase Space and its Poisson-Lie Groupoid

Abstract

The precise relationship between the arbitrary monodromy dependent 2-form appearing in the chiral WZNW symplectic form and the `exchange r-matrix' that governs the corresponding Poisson brackets is established. Generalizing earlier results related to diagonal monodromy, the exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter equation, which is found to admit an interpretation in terms of (new) Poisson-Lie groupoids. Dynamical exchange r-matrices for which right multiplication yields a classical or a Poisson-Lie symmetry on the chiral WZNW phase space are presented explicitly.

arXiv comment13 pages, LaTeX, minor typos corrected

References in corpus (5)

• Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
• Lattice Wess-Zumino-Witten Model and Quantum Groups
• Dressing Symmetries
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
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Cited by in corpus (10)

• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids
• On dynamical r-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras
• Quantum matrix algebra for the SU(n) WZNW model
• Generalizations of Felder's elliptic dynamical r-matrices associated with twisted loop algebras of self-dual Lie algebras
• A note on a canonical dynamical r-matrix
• Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
• Classical Wakimoto Realizations of Chiral WZNW Bloch Waves
• Trigonometric dynamical r-matrices over Poisson Lie base
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes