Exact structures and degeneration of Hall algebras

Exact structures and degeneration of Hall algebras

We study degenerations of the Hall algebras of exact categories induced by degree functions on the set of isomorphism classes of indecomposable objects. We prove that each such degeneration of the Hall algebra H(E) of an exact category E is the Hall algebra of a smaller exact structure E′

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2022-03, Vol.398, p.108210, Article 108210
Hauptverfasser: Fang, Xin, Gorsky, Mikhail
Format: Artikel
Sprache:eng
Schlagworte:
Category Theory
Degeneration
Exact structure
Hall algebra
Mathematics
Quantum Algebra
Representation Theory
Rings and Algebras
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Beschreibung
Zusammenfassung:We study degenerations of the Hall algebras of exact categories induced by degree functions on the set of isomorphism classes of indecomposable objects. We prove that each such degeneration of the Hall algebra H(E) of an exact category E is the Hall algebra of a smaller exact structure E′
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2022.108210