半导出Hall代数的Gr(o)bner-Shirshov基

在Dynkin型Ringel-Hall代数中,不可分解表示同构类之间的所有拟交换关系之集构成由这些关系生成的理想的一个极小Gr(o)bner-Shirshov基,并且相应的不可约元素构成此Ringel-Hall代数的一组PBW基.本文的目的 是将把此结果推广到Dynkin箭图的半导出Hall代数上去.为此,首先通过计算...

Grobner-Shirshov Basis of Semi-derived Hall Algebras

In Ringel-Hall algebra of Dynkin type,the set of skew commutator relations between the isomorphism classes of indecomposable representations form a minimal GrobnerShirshov basis for the ideal generated by these relations and the set of corresponding irreducible elements gave a PBW-type basis of the Ringel-Hall algebra.The aim of this paper is to generalize this result to the semi-derived Hall algebra of Dynkin quivers.First,a minimal Grobner-Shirshov basis for the semi-derived Hall algebra of Dynkin quivers is given by computing possible compositions between the skew commutator relations.Then,by taking the corresponding irreducible monomials,a PBW-type basis of the semi-derived Hall algebra of Dynkin quivers is given.