Gröbner–Shirshov Basis of Derived Hall Algebra of Type An
| Autor: | Abdukadir Obul, Zhe He |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Commutator
Derived category Pure mathematics Applied Mathematics General Mathematics Mathematics::Rings and Algebras 010102 general mathematics Quiver 010103 numerical & computational mathematics Basis (universal algebra) Type (model theory) 01 natural sciences Hall algebra Bounded function 0101 mathematics Mathematics::Representation Theory Indecomposable module Mathematics |
| Zdroj: | Acta Mathematica Sinica, English Series. 36:929-942 |
| ISSN: | 1439-7617 1439-8516 |
| DOI: | 10.1007/s10114-020-9547-2 |
| Popis: | 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 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). |
| Databáze: | OpenAIRE |
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