On The Center Of Two-parameter Quantum Groups U_{r, S}(G₂)

In this paper,let K be an algebraically closed field of characteristic of 0 and fix non-zero elements r, s in the field of K. Here we assume r≠s. According to the algebraic construction and the representation theory of Ur,s(G2),we define an invariant form on Ur,s(G2).Finally we introduce an analogue of the Harish-Chandra homomorphism and use it to determine the center of two-parameter quantum group Ur,s(G2) that is isomorphic to a polynomial algebra with two variables.