Explicit generators and relations for the centre of the quantum group

For the standard Drinfeld-Jimbo quantum group Uqpgq associated with a simple Lie algebra g, we construct explicit generators of the centre ZpUqpgqq, and determine the relations satisfied by the generators. For g of type Anpn ě 2q, D2k`1pk ě 2q or E6, the centre ZpUqpgqq is isomorphic to a quotient of a polynomial algebra in multiple variables, which is described in a uniform manner for all cases. For g of any other type, ZpUqpgqq is generated by n “rankpgq algebraically independent elements.