On cluster algebras from unpunctured surfaces with one marked point
Ilke Canakci, Kyungyong Lee, Ralf Schiffler
TL;DR
This paper extends the theory of cluster algebras from unpunctured surfaces to cases with a single marked point, establishing the equality of the cluster algebra and the upper cluster algebra.
Contribution
It introduces a construction of canonical bases for these cluster algebras with one marked point and proves their equality with upper cluster algebras.
Findings
Canonical bases constructed for cluster algebras with one marked point
Proves cluster algebra equals upper cluster algebra in this case
Extends previous results from multiple to single marked point surfaces
Abstract
We extend the construction of canonical bases for cluster algebras from unpunctured surfaces to the case where the number of marked points is one, and we show that the cluster algebra is equal to the upper cluster algebra in this case.
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