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On quantum cluster algebras of finite type
Published 7 Nov 2010 in math.RT, math.QA, and math.RA | (1011.1606v2)
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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