  The central elements of the algebra of monodromy matrices associated with the
$\mathbb{Z}_n$ R-matrix are studied. When the crossing parameter $w$ takes a
special rational value $w=\frac{n}{N}$, where $N$ and $n$ are positive coprime
integers, the center is substantially larger than that in the generic case for
which the "quantum determinant" provides the center. In the trigonometric
limit, the situation corresponds to the quantum group at roots of unity. This
is a higher rank generalization of the recent results by Belavin and Jimbo.
