Gr"{o}bner-Shirshov Basis of Quantum Group of Type $mathbb{D}_4$ |
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| Authors: | Gulshadam YUNUS and Abdukadir OBUL |
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| Affiliation: | [1]College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China [2]Corresponding author. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China |
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| Abstract: | The authors take all isomorphism classes of indecomposable representations as new generators, and obtain all skew-commutators between these generators by using the Ringel-Hall algebra method. Then they prove that the set of these skew-commutators is a Gröbner-Shirshov basis for quantum group of type (mathbb{D}_4). |
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| Keywords: | Ringel-Hall algebra Indecomposable modules GrSbner-Shirshov basis Compositions |
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