论文标题
响应大厅代数的量子集群字符
Quantum cluster characters of Hall algebras revisited
论文作者
论文摘要
令$ q $为有限的无环有价箭量。我们定义了与$ q $的射影表示形态类别相关的霍尔代数上的Bialgebra结构和集成图。作为应用程序，我们恢复了\ cite {dxz}中定义的过滤性同态，它实现了主要系数量子群集代数$ \ a_q（q）$作为形态学的霍尔代数的子味。此外，我们还恢复了caldero-chapoton公式，以及量子Caldero之间的一些乘法公式 - chapoton字符。
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.
