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arXiv · 1011.1606

On quantum cluster algebras of finite type

Ming Ding
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Abstract

We extend the definition of a quantum analogue of the Caldero-Chapoton map defined in \cite{rupel}. When $Q$ is a quiver of finite type, we prove that the algebra $\mathcal{AH}_{|k|}(Q)$ generated by all cluster characters (see Definition \ref{def}) is exactly the quantum cluster algebra $\mathcal{EH}_{|k|}(Q)$.

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Ming Ding. 2010-11-07. On quantum cluster algebras of finite type. https://doi.org/10.1007/s11464-011-0104-2

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