On the center of two-parameter quantum groups

Abstract

We describe Poincaré–Birkhoff–Witt bases for the two-parameter quantum groups U = U_{r,s}(sln) following Kharchenko and show that the positive part of U has the structure of an iterated skew polynomial ring. We define an ad-invariant bilinear form on U, which plays an important role in the construction of central elements. We introduce an analogue of the Harish-Chandra homomorphism and use it to determine the centre of U.