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Gröbner-Shirshov basis of quantum group of type \(\mathbb{D}_4\)

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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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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Gulshadam Yunus & Abdukadir Obul

Authors
  1. Gulshadam Yunus
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  2. Abdukadir Obul
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Correspondence to Abdukadir Obul.

Additional information

Project supported by the Natural Science Foundation of Xinjiang University (the Starting Research Fund for Doctors) (No.BS080103).

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Yunus, G., Obul, A. Gröbner-Shirshov basis of quantum group of type \(\mathbb{D}_4\) . Chin. Ann. Math. Ser. B 32, 581–592 (2011). https://doi.org/10.1007/s11401-011-0656-1

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  • DOI: https://doi.org/10.1007/s11401-011-0656-1

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