| Gr?bner–Shirshov Basis of Derived Hall Algebra of Type A_n |
| |
| 基金项目： | Supported by the Natural Science Foundation of China (Grant No. 11861061) |
| |
| 摘 要： | 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 Gr?bner–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(A_n) of type A_n. First, we compute all skew commutator relations between the iso-classes of indecomposable objects in the bounded derived category D~b(A_n) using the Auslander–Reiten quiver of D~b(A_n), 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(A_n).
|
Gröbner-Shirshov Basis of Derived Hall Algebra of Type An |
| |
| Authors: | Zhe HE Abdukadir OBUL |
| |
| Institution: | College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China |
| |
| Abstract: | 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 Gröbner-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 Db(An) using the Auslander-Reiten quiver of Db(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). |
| |
| Keywords: | Derived Hall algebra indecomposable objects skew commutator relations Auslander-Reiten quiver |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学学报(英文版)》下载免费的PDF全文 |
