The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective al...The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described.展开更多
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 National Natural Science Foundation of China (No. 10801099)the Zhejiang Provincial Natural Science Foundation of China (No. J20080154)the grant from Science Technology Department of Zhejiang Province (No. 2011R10051)
文摘The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described.
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).
