The chiral WZNW phase space and its Poisson-Lie groupoid

The precise relationship between the arbitrary monodromy dependent 2-form a ppearing in the chiral WZNW symplectic form and the 'exchange r-matrix' tha t governs the corresponding Poisson brackets is established. Generalizing e arlier results related to diagonal monodromy, the exchange r-matrices are s hown to satisfy a new dynamical generalization of the classical modified Ya ng-Baxter equation, which is found to admit an interpretation in terms of ( new) Poisson-Lie groupoids. Dynamical exchange r-matrices for which right m ultiplication yields a classical or a Poisson-Lie symmetry on the chiral WZ NW phase space are presented explicitly. (C) 1999 Published by Elsevier Sci ence B.V. All rights reserved.