Acyclic quantum cluster algebras via Hall algebras of morphisms

22 Nov 2019 · Ding Ming, Xu Fan, Zhang Haicheng ·

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.