PBW Basis of the Modified Ringel–Hall Algebra of Type An via Gröbner–Shirshov Basis

Desheng Hu, Abdukadir Obul and Naihuan Jing

Journal of Mathematics, 2023, vol. 2023, 1-27

Abstract: In the Ringel–Hall algebra of Dynkin type, the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Gröbner–Shirshov basis, and the set of the corresponding irreducible elements forms a PBW-type basis of the Ringel–Hall algebra. The aim of this paper is to generalize this result to the modified Ringel–Hall algebra of type. First, we compute a minimal Gröbner–Shirshov basis for the modified Ringel–Hall algebra of type An by proving all possible compositions between the commutator relations are trivial. Then, by taking the corresponding irreducible monomials, we construct a PBW-type basis for the modified Ringel–Hall algebra of type An.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2023/6820173.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2023/6820173.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6820173

DOI: 10.1155/2023/6820173

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().