The Chiral WZNW Phase Space and its Poisson-Lie Groupoid

Details The Chiral WZNW Phase Space and its Poisson-Lie Groupoid The Chiral WZNW Phase Space and its Poisson-Lie Groupoid

1999-07-08

arxiv.org/abs/hep-th/9907050v2

Phys.Lett. B463 (1999) 83-92

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTeX, minor typos corrected

Scientific paper

10.1016/S0370-2693(99)00965-X

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.

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