On a Quantum Analog of the Caldero–Chapoton Formula

@article{Rupel2010OnAQ,
  title={On a Quantum Analog of the Caldero–Chapoton Formula},
  author={Dylan Rupel},
  journal={International Mathematics Research Notices},
  year={2010},
  volume={2011},
  pages={3207-3236}
}
  • Dylan Rupel
  • Published 12 March 2010
  • Mathematics
  • International Mathematics Research Notices
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. 
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