2023
DOI: 10.1155/2023/6820173
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PBW Basis of the Modified Ringel–Hall Algebra of Type A n via Gröbner–Shirshov Basis

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 … Show more

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