On a Poisson-Lie analogue of the classical dynamical Yang-Baxter equation for self-dual Lie algebras

摘要

We derive a generalization of the classical dynamical Yang-Baxter equation(CDYBE) on a self-dual Lie algebra $\cal G$ by replacing the cotangent bundleT^*G in a geometric interpretation of this equation by its Poisson-Lie (PL)analogue associated with a factorizable constant r-matrix on $\cal G$. Theresulting PL-CDYBE, with variables in the Lie group G equipped with theSemenov-Tian-Shansky Poisson bracket based on the constant r-matrix, coincideswith an equation that appeared in an earlier study of PL symmetries in the WZNWmodel. In addition to its new group theoretic interpretation, we present aself-contained analysis of those solutions of the PL-CDYBE that were found inthe WZNW context and characterize them by means of a uniqueness result under acertain analyticity assumption.