B2-型modified Ringel-Hall代数的Gröbner-Shirshov基

doi:10.6040/j.issn.1671-9352.0.2022.200

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (2): 33-43.doi: 10.6040/j.issn.1671-9352.0.2022.200

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B₂-型modified Ringel-Hall代数的Gröbner-Shirshov基

胡德胜,阿布都卡的·吾甫^*

新疆大学数学与系统科学学院, 新疆乌鲁木齐 830046

发布日期:2023-02-12
作者简介:胡德胜(1995— ),男,硕士研究生,研究方向为代数表示论、量子群及Gröbner-Shirshov基理论. E-mail:2318726727@qq.com*通信作者简介:阿布都卡的·吾甫(1963— ),男,博士,教授,研究方向为代数表示论、量子群及Gröbner-Shirshov基理论. E-mail:abdukadir@xju.edu.cn
基金资助:
国家自然科学基金资助项目(11861061)

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

HU De-sheng, Abdukadir OBUL^*

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

Published:2023-02-12

摘要/Abstract

摘要： 给出了modified Ringel-Hall代数中不可分解复形同构类之间的所有拟交换关系,证明了这些拟交换关系之集是B2-型modified Ringel-Hall代数的一个极小Gröbner-Shirshov基。作为一个应用,得到了B2-型modified Ringel-Hall代数的一组PBW基。

关键词: modified Ringel-Hall代数, 拟交换关系, Grö, bner-Shirshov基

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

中图分类号:

O153.3

胡德胜,阿布都卡的·吾甫. B₂-型modified Ringel-Hall代数的Gröbner-Shirshov基[J]. 《山东大学学报(理学版)》, 2023, 58(2): 33-43.

HU De-sheng, Abdukadir OBUL. Gröbner-Shirshov basis of modified Ringel-Hall algebra of type B₂[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(2): 33-43.

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B₂-型modified Ringel-Hall代数的Gröbner-Shirshov基

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

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