再论Hall代数的量子团特征
Quantum cluster characters of Hall algebras revisited
摘要：
设$Q$是有限非循环值的整数。我们定义了一个双代数结构和整合映射的霍尔代数相关的态射范畴的投影表示的$Q$。作为应用，我们恢复了\cite{DXZ}中定义的满同态，它实现了主系数量子簇代数$\A_q(Q)$作为态射的Hall代数的子商.此外，我们还恢复了量子Caldero-Chapoton公式，以及量子Caldero-Chapoton特征标之间的一些乘法公式。
英文摘要：
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 \cite{DXZ}, which realizes the principal coefficient quantum cluster algebra $\A_q(Q)$ 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.
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