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

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

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.