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arXiv · 1109.5342

Multiplicative properties of a quantum Caldero-Chapoton map associated to valued quivers

Ming Ding·Jie Sheng
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Abstract

We prove a multiplication theorem of a quantum Caldero-Chapoton map associated to valued quivers which extends the results in \cite{DX}\cite{D}. As an application, when $Q$ is a valued quiver of finite type or rank 2, we obtain that the algebra $\mathcal{AH}_{|k|}(Q)$ generated by all cluster characters (see Definition \ref{def}) is exactly the quantum cluster algebra $\mathcal{EH}_{|k|}(Q)$ and various bases of the quantum cluster algebras of rank 2 can naturally be deduced.

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BibTeXRIS

Ming Ding, Jie Sheng. 2011-09-25. Multiplicative properties of a quantum Caldero-Chapoton map associated to valued quivers. https://arxiv.org/abs/1109.5342

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