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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. © 2016, Beijing University of Technology. All right reserved.
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