On quantum cluster algebras of finite type

Details On quantum cluster algebras of finite type On quantum cluster algebras of finite type

2010-11-07

arxiv.org/abs/1011.1606v2

Mathematics

Representation Theory

9 pages

Scientific paper

10.1007/s11464-011-0104-2

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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