Quantum cluster characters of Hall algebras revisited

Changjian Fu ^[1] ; Liangang Peng ^[1] ; Haicheng Zhang ^[2]
1. [1] Sichuan University
  
  Sichuan University
  
  China
2. [2] Nanjing Normal University
  
  Nanjing Normal University
  
  China
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 1, 2023
Idioma: inglés
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Resumen
- Let Q be a finite acyclic valued quiver. We define a bialgebra structure and an integration map on the Hall algebra associated to the morphism category of projective representations of Q. As an application, we recover the surjective homomorphism defined in [12], which realizes the principal coefficient quantum cluster algebra Aq(Q) as a sub-quotient of the Hall algebra of morphisms. Moreover, we also recover the quantum Caldero–Chapoton formula, as well as some multiplication formulas between quantum Caldero–Chapoton characters.