defining structure of two-parameter quantum group corresponding to the exceptional Lie algebra G2. In CH.4, we obtain a realization of Ur,s(G2). In CH.5, we give Lusztig's Q-isomorphisms from Ur,s(G2) to its associated quantum group Us-1,r-1(G2).Recently, Prof. Naihong Hu and Dr. Hongliang Zhang have found the defining structure of two-parameter quantum group associated to the affine Lie algebra of type A.
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