%0 Journal Article
%T A Uniqueness Property for the Quantization of Teichm¨šller Spaces
%A Hua Bai
%J Mathematics
%D 2005
%I arXiv
%X Chekhov, Fock and Kashaev introduced a quantization of the Teichm\"{u}ller 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 Teichm\"{u}ller 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.
%U http://arxiv.org/abs/math/0509679v1