On Quantum Analogue of The Caldero-Chapoton Formula

Details On Quantum Analogue of The Caldero-Chapoton Formula On Quantum Analogue of The Caldero-Chapoton Formula

2010-03-12

arxiv.org/abs/1003.2652v5

Mathematics

Quantum Algebra

Scientific paper

10.1093/imrn/rnq192

Let $Q$ be any invertible valued quiver without oriented cycles. We study connections between the category of valued representations of $Q$ and expansions of cluster variables in terms of the initial cluster in quantum cluster algebras. We show that an analogue of the Caldero-Chapoton formula holds for all quantum cluster algebras of finite type and for any cluster variable in an almost acyclic cluster.

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