Gr&#246;bner-Shirshov Basis of Quantum Group <italic>U<sub>q</sub></italic>(<italic>C</italic><sub>3</sub>) and Its Irreducible Modules

GAO Zhenzhen; YANG Shilin; WUFU Abudoukade

doi:10.11936/bjutxb2015060053

GAO Zhenzhen, YANG Shilin, WUFU Abudoukade. Gröbner-Shirshov Basis of Quantum Group Uq(C3) and Its Irreducible Modules[J]. Journal of Beijing University of Technology, 2016, 42(4): 632-636. DOI: 10.11936/bjutxb2015060053

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Gröbner-Shirshov Basis of Quantum Group U_q(C₃) and Its Irreducible Modules

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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 U_q(C₃) was constructed. Then, a Gröbner-Shirshov basis of finite dimensional irreducible modules of U_q(C₃) was given by using double free module and composition lemma.

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Gröbner-Shirshov Basis of Quantum Group Uq(C3) and Its Irreducible Modules

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Gröbner-Shirshov Basis of Quantum Group U_q(C₃) and Its Irreducible Modules