English

On Quantum Analogue of The Caldero-Chapoton Formula

Quantum Algebra 2013-09-11 v5 Rings and Algebras Representation Theory

Abstract

Let QQ be any invertible valued quiver without oriented cycles. We study connections between the category of valued representations of QQ 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.

Keywords

Cite

@article{arxiv.1003.2652,
  title  = {On Quantum Analogue of The Caldero-Chapoton Formula},
  author = {Dylan Rupel},
  journal= {arXiv preprint arXiv:1003.2652},
  year   = {2013}
}