Volume 9, issue 3 (2009)

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Quantum Teichmüller space and Kashaev algebra

Ren Guo and Xiaobo Liu

Algebraic & Geometric Topology 9 (2009) 1791–1824
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.

Keywords
Teichmüller space, quantization, Kashaev coordinates, noncommutative algebra
Mathematical Subject Classification 2000
Primary: 57R56
Secondary: 57M50, 20G42
References
Publication
Received: 6 May 2009
Accepted: 20 August 2009
Published: 27 September 2009
Authors
Ren Guo
School of Mathematics
University of Minnesota
Minneapolis
MN 55455
USA
Xiaobo Liu
Department of Mathematics
Columbia University
2990 Broadway
New York
NY 10027
USA