Acyclic quantum cluster algebras via Hall algebras of morphisms

Acyclic quantum cluster algebras via Hall algebras of morphisms

Let A be the path algebra of a finite acyclic quiver Q over a finite field. We realize the quantum cluster algebra with principal coefficients associated to Q as a sub-quotient of a certain Hall algebra involving the category of morphisms between projective A -modules.

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Veröffentlicht in:Mathematische Zeitschrift 2020-12, Vol.296 (3-4), p.945-968
Hauptverfasser: Ding, Ming, Xu, Fan, Zhang, Haicheng
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Clusters
Fields (mathematics)
Mathematics
Mathematics and Statistics
Quotients
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Beschreibung
Zusammenfassung:Let A be the path algebra of a finite acyclic quiver Q over a finite field. We realize the quantum cluster algebra with principal coefficients associated to Q as a sub-quotient of a certain Hall algebra involving the category of morphisms between projective A -modules.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02465-0