Quantum Teichm\"uller space and Kashaev algebra
Ren Guo, Xiaobo Liu
TL;DR
This paper explores the relationship between quantum Teichmüller space and Kashaev algebra, showing how coordinate transformations connect these structures in the context of quantum geometry.
Contribution
It establishes a natural relationship between quantum Teichmüller space and generalized Kashaev algebra via coordinate transformations.
Findings
Connection between shear and Kashaev coordinates
Generalized Kashaev algebra for complex parameters
Quantum Teichmüller space linked to Kashaev algebra
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 Teichm\"uller space and the generalized Kashaev algebra.
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