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

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

2011-09-25

arxiv.org/abs/1109.5342v1

Mathematics

Representation Theory

12 pages

Scientific paper

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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