JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 33-43.doi: 10.6040/j.issn.1671-9352.0.2022.200

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Gröbner-Shirshov basis of modified Ringel-Hall algebra of type B2

HU De-sheng, Abdukadir OBUL*   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China
  • Published:2023-02-12

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Abstract: Skew commutator relations between the isoclasses of indecomposable complexes in the modified Ringel-Hall algebra of type B2 is computed, it is proved that the set of these skew commutator relations forms a minimal Gröbner-Shirshov basis for the modified Ringel-Hall algebra of type B2. As an application, a PBW-type basis of the modified Ringel-Hall algebra of type B2 is obtained.

Key words: modified Ringel-Hall algebra, skew commutator relation, Grö, bner-Shirshov basis

CLC Number: 

  • O153.3
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