B_(2)-型modified Ringel-Hall代数的Gröbner-Shirshov基  

Gröbner-Shirshov basis of modified Ringel-Hall algebra of type B_(2)

作　　者：胡德胜 阿布都卡的·吾甫[1] HUDe-sheng;Abdukadir OBUL(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,Xinjiang,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《山东大学学报（理学版）》2023年第2期33-43,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11861061)。

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B_(2)-型modified Ringel-Hall代数的一个极小Gröbner-Shirshov基。作为一个应用,得到了B_(2)-型modified Ringel-Hall代数的一组PBW基。Skew commutator relations between the isoclasses of indecomposable complexes in the modified Ringel-Hall algebra of type B_(2) 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 B_(2).As an application,a PBW-type basis of the modified Ringel-Hall algebra of type B_(2) is obtained.

关 键 词：modified Ringel-Hall代数 拟交换关系 Gröbner-Shirshov基 

分 类 号：O153.3[理学—数学]