为了研究量子群Uq ( C3)及其有限维不可约模的Gröbner-Shirshov基，基于赋值图C3的Auslander-Reiten理论和表示的Gröbner-Shirshov基理论，运用Ringel-Hall代数方法，构造了量子群Uq ( C3)的Gröbner-Shirshov基，进而用双自由模及钻石-合成引理，给出量子群Uq ( C3)的有限维不可约模的Gröbner-Shirshov基。%Based on Auslander-Reiten theory of valued graph C3 and Gröbner-Shirshov bases for representation theory, First by using the Ringel-Hall algebra approach, a Gröbner-Shirshov basis of quantum group Uq ( C3 ) was constructed. Then, a Gröbner-Shirshov basis of finite dimensional irreducible modules of Uq ( C3 ) was given by using double free module and composition lemma.
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