4 papers
Band bases as common triangular bases in cluster algebras from surfaces
Fan Qin, Chao Shen
We consider the skein algebra of an unpunctured marked surface. Thurston previously constructed its band basis topologically. We show that this band basis coincides with the common…
From i-boxes to signed words
Alessandro Contu, Fan Qin, Qiaoling Wei
The combinatorics of i-boxes has recently been introduced by Kashiwara--Kim--Oh--Park in the study of cluster algebras arising from the representation theory of quantum affine alge…
Stability scattering diagrams and quiver coverings
Qiyue Chen, Travis Mandel, Fan Qin
Given a covering of a quiver (with potential), we show that the associated Bridgeland stability scattering diagrams are related by a restriction operation under the assumption of a…
Applications of the freezing operators on cluster algebras
Fan Qin
We apply freezing operators to relate different (quantum) upper cluster algebras. We prove that these operators send localized (quantum) cluster monomials to localized (quantum) cl…