  For a slightly generalised version of the Jimbo quantum group associated with
any finite dimensional simple Lie algebra $\mathfrak{g}$, we show that its
centre is a polynomial algebra. We construct a set of algebraically independent
central elements, each associated with a fundamental weight of $\mathfrak{g}$,
and prove that they generate the entire centre of the quantum group. A key
ingredient in the proofs of these results is a quantum Harish-Chandra
isomorphism for the generalised quantum group, which is proven in some details.
