2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95184Chekhov, Fock and Kashaev introduced a quantization of the Teichmüller space $\mathcal{T}^q(S)$ of a punctured surface $S$, and an exponential version of this construction was developed by Bonahon and Liu. The construction of the quantum Teichmüller space crucially depends on certain coordinate change isomorphisms between the Chekhov-Fock algebras associated to different ideal triangulations of $S$. We show that these coordinate change isomorphisms are essentially unique, once we require them to satisfy a certain number of natural conditions.14 pages, 3 figuresGeometric TopologyQuantum Algebra57M50; 57R56; 20G42text