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.)



Does There Exists a General Quantum Casimir Extending the $U_q({\mathfrak sl}_2$ Case? 
The centers of the Drinfeld-Jimbo quantum groups $U\_q(\mathfrak{g})$ are well-understood and quite analogous to the classical case. See the book by Klimyk and Schmüdgen, Section 6.3, where in particular the quantum Casimirs are constructed. 


