Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 9, Number 3 (2009), 1791-1824.
Quantum Teichmüller space and Kashaev algebra
Ren Guo and Xiaobo Liu
Abstract
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
Source
Algebr. Geom. Topol., Volume 9, Number 3 (2009), 1791-1824.
Dates
Received: 6 May 2009
Accepted: 20 August 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
https://projecteuclid.org/euclid.agt/1513797044
Digital Object Identifier
doi:10.2140/agt.2009.9.1791
Mathematical Reviews number (MathSciNet)
MR2550095
Zentralblatt MATH identifier
1181.57034
Subjects
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]
Keywords
Teichmüller space quantization Kashaev coordinates noncommutative algebra
Citation
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. https://projecteuclid.org/euclid.agt/1513797044