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arXiv · hep-th/9907050

The Chiral WZNW Phase Space and its Poisson-Lie Groupoid

J. Balog·L. Feher·L. Palla
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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.

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J. Balog, L. Feher, L. Palla. 1999-10-13. The Chiral WZNW Phase Space and its Poisson-Lie Groupoid. https://doi.org/10.1016/s0370-2693(99)00965-x

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