Abstract

It is shown that the fundamental Poisson brackets in the chiral sectors of WZNW theory and its Liouville-Toda reduction are of the r-matrix form. In general, the r-matrix is monodromy dependent, but in the case of A l Lie algebras, and only then, this monodromy dependence can be “gauged away” by choosing appropriate representatives in the conjugacy classes of the monodromy. The resulting non-trivial solution of the classical Yang-Baxter equation is the classical limit of the quantum R-matrix of A l Toda theory found recently by Cremmer and Gervais.

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