We know that in Ringel-Hall algebra of Dynkin type,the set of all skew commutator relations between the iso-classes of indecomposable modules forms a minimal Grobner-Shirshov basis,and the corresponding irreducible el...We know that in Ringel-Hall algebra of Dynkin type,the set of all skew commutator relations between the iso-classes of indecomposable modules forms a minimal Grobner-Shirshov basis,and the corresponding irreducible elements forms a PBW type basis of the Ringel-Hall algebra.We aim to generalize this result to the derived Hall algebra DH(An)of type An.First,we compute all skew commutator relations between the iso-classes of indecomposable objects in the bounded derived category D^b(An)using the Auslander-Reiten quiver of D^b(An),and then we prove that all possible compositions between these skew commutator relations are trivial.As an application,we give a PBW type basis of DH(An).展开更多
基金Supported by the Natural Science Foundation of China(Grant No.11861061)。
文摘We know that in Ringel-Hall algebra of Dynkin type,the set of all skew commutator relations between the iso-classes of indecomposable modules forms a minimal Grobner-Shirshov basis,and the corresponding irreducible elements forms a PBW type basis of the Ringel-Hall algebra.We aim to generalize this result to the derived Hall algebra DH(An)of type An.First,we compute all skew commutator relations between the iso-classes of indecomposable objects in the bounded derived category D^b(An)using the Auslander-Reiten quiver of D^b(An),and then we prove that all possible compositions between these skew commutator relations are trivial.As an application,we give a PBW type basis of DH(An).
