As is well known (see Kassel), when $q$ is not a root of unity, the centre or the quantum enveloping algebra $U_q({\mathfrak sl}_2)$ of ${\mathfrak sl}_2$ is generated by the element $$ C_q = EF + \frac{q^{-1}K+qK^{-1}}{(q-q^{-1})^2}. $$ The element is called the quantum Casimir. My questions are as follows:

(i) Does this situation extend to the general setting of $U_q({\mathfrak sl}_N)$?

(ii) If it does, is there a general formula for $C_q$?

(iii) How would this formula relate to the usual formula for the classical Casimir? (The uasual formula I refer to is $\sum X^iX_i$, for some basis $X_i$ and its dual $X^i$, see wikipedia for details.)