Quantum-group-invariant integrable n-state vertex models with periodic boundary conditions

An U _q(sl( n))-invariant transfer matrix with periodic boundary conditions is analysed by means of the algebraic nested Bethe ansatz for the case of q being a root of unity. The transfer matrix corresponds to a two-dimensional vertex model on a torus with topological interaction with respect to the three-dimensional interior of the torus. By means of finite-size analysis we find the central charge of the corresponding Virasoro algebra as c = (n - 1) [ {1 - n(n + 1)}/{(r(r - 1))}] .