The centre of the graph and moduli algebras at roots of 1

Abstract

The structure of the centres Z(Lg) and Z(Mg) of the graph algebra Lg(sl2) and the moduli algebraMg(sl2) is studied at roots of 1. It it shown that Z(Lg) can be endowed with the structure of the Poisson graph algebra. The elements of Spec(Z(Mg)) are shown to satisfy the defining relation for the holonomies of a flat connection along the cycles of a Riemann surface. The irreducible representations of the graph algebra are constructed.