On quantum cluster algebras of finite type

Abstract

We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When Q is a quiver of finite type, we prove that the algebra {\mathscr{H}}_{\left|k\right|}\left(Q\right) generated by all cluster characters is exactly the quantum cluster algebra ℰ{\mathscr{H}}_{\left|k\right|}\left(Q\right).

Keywords

Cluster variable / quantum cluster algebra

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg