On The Center Of Two-parameter Quantum Groups With Even Rank

In this paper,we mainly consider the center of one class of two-parameter quantum groups Ur,s(g)corresponding to complex semisimple Lie algebras g through the HarishChandra homomorphism.Based on the Rosso form and the representation theory of weight modules established by Bergeron-Gao-Hu and Pei-Hu-Rosso,we prove that the Harish-Chandra homomorphism of any two-parameter quantum group with even rank is an isomorphism.