Quantum Teichmüller space and Kashaev algebra

Guo, Ren; Liu, Xiaobo

doi:10.2140/agt.2009.9.1791

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Quantum Teichmüller space and Kashaev algebra

Ren Guo and Xiaobo Liu

Algebraic & Geometric Topology 9 (2009) 1791–1824

DOI: 10.2140/agt.2009.9.1791

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

Volume 9, issue 3 (2009)