Kashaev algebra associated to a surface is a noncommutative deformation of the algebra of rational functions of Kashaev coordinates. For two arbitrary complex numbers, there is a generalized Kashaev algebra. The relationship between the shear coordinates and Kashaev coordinates induces a natural relationship between the quantum Teichmüller space and the generalized Kashaev algebra.
"Quantum Teichmüller space and Kashaev algebra." Algebr. Geom. Topol. 9 (3) 1791 - 1824, 2009. https://doi.org/10.2140/agt.2009.9.1791