On the Center of Two-parameter Quantum Groups $U_{r,s}(\mathfrak{so}_{2n+1})$

Abstract

The paper mainly considers the center of two-parameter quantum groups $U_{r,s}(\mathfrak{so}_{2n+1})$ via an analogue of the Harish-Chandra homomorphism. In the case when $n$ is odd, the Harish-Chandra homomorphism is not injective in general. When $n$ is even, the Harish-Chandra homomorphism is injective and the center of two-parameter quantum groups $U_{r,s}{(\mathfrak{so}_{2n+1})}$ is described, up to isomorphism.