On classification of dynamical r-matrices

Abstract

Using recent results of P. Etingof and A. Varchenko on the Classical Dynamical Yang-Baxter equation, we reduce the classification of dynamical r-matrices r on a commutative subalgebra l of a Lie algebra g to a purely algebraic problem under some technical conditions on the symmetric part of r. Using this, we then classify all non skew-symmetric dynamical r-matrices when g is a simple Lie algebra and l a commutative subalgebra containing a regular semisimple element. This partially answers a question in [EV] q-alg/9703040 and generalizes the Belavin-Drinfeld classification of constant r-matrices. This classification is similar and in some sense simpler than the Belavin-Drinfeld classification.