Quantum cluster algebra realization for stated ${\mathrm{SL}}_n$-skein algebras and rotation-invariant bases for polygons

Peigen Cao, Min Huang, Zhihao Wang

We construct a quantum cluster structure on the skew-field of fractions $\mathrm{Frac}({\mathcal{S}}_{\ddot{I}}‰(\mathfrak{S}))$ of the stated ${\mathrm{SL}}_n$-skein algebra ${\mathscr S}_ω(\mathf…