On the moduli space of classical dynamical r-matrices

Abstract

We define and study the moduli space of classical dynamical r-matrices associated to a Lie algebra g and a subalgebra l of g. As opposed to the previous papers q-alg/9703040 and q-alg/9706017 we do not make any commutativity assumption on the subalgebra l. We extend the notion of gauge-transformation to this setting and show that, under some technical conditions, the space of dynamical r-matrices modulo gauge-transformations is isomorphic to an explicitly given affine variety.