On a Quantum Analog of the Caldero–Chapoton Formula

By Dylan Rupel. 2010

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Let Q be any valued quiver without oriented cycles. We study connections between the category of valued representations of Q and expansions of cluster variables in terms of an initial cluster in quantum cluster algebras. We show that an analog of the Caldero–Chapoton formula holds for the specializations , where is a finite field, in all quantum cluster algebras of finite type, including nonsimply laced types, and for any cluster variable in an almost acyclic cluster.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9800e39e99fdc698010c0691d40c4446dab9dad6