53 citations · 204 across the 31 of their papers we have counts for
5 papers · 1 filter
Quantum Teichmüller space and Kashaev algebra
Ren Guo, Xiaobo Liu
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 g…
Local representations of the quantum Teichmuller space
Hua Bai, Francis Bonahon, Xiaobo Liu
We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choi…
Quantum hyperbolic invariants for diffeomorphisms of small surfaces
Xiaobo Liu
An earlier article with Francis Bonahon introduced new invariants for pseudo-Anosov diffeomorphisms of surface, based on the representation theory of the quantum Teichmuller space.…
The quantum Teichmuller space as a noncommutative algebraic object
Xiaobo Liu
We consider the quantum Teichmuller space of the punctured surface introduced by Chekhov-Fock-Kashaev, and formalize it as a noncommutative deformation of the space of algebraic fu…
Representations of the quantum Teichmuller space, and invariants of surface diffeomorphisms
Francis Bonahon, Xiaobo Liu
We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the…