Algebraic & Geometric Topology

Quantum Teichmüller space and Kashaev algebra

Ren Guo and Xiaobo Liu

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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.

Article information

Algebr. Geom. Topol., Volume 9, Number 3 (2009), 1791-1824.

Received: 6 May 2009
Accepted: 20 August 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R56: Topological quantum field theories
Secondary: 57M50: Geometric structures on low-dimensional manifolds 20G42: Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]

Teichmüller space quantization Kashaev coordinates noncommutative algebra


Guo, Ren; Liu, Xiaobo. Quantum Teichmüller space and Kashaev algebra. Algebr. Geom. Topol. 9 (2009), no. 3, 1791--1824. doi:10.2140/agt.2009.9.1791.

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