Volume 7, issue 3 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Quantum Teichmüller spaces and Kashaev's $6j$–symbols

Hua Bai

Algebraic & Geometric Topology 7 (2007) 1541–1560
Abstract

The Kashaev invariants of 3–manifolds are based on 6j–symbols from the representation theory of the Weyl algebra, a Hopf algebra corresponding to the Borel subalgebra of Uq(sl(2, )). In this paper, we show that Kashaev’s 6j–symbols are intertwining operators of local representations of quantum Teichmüller spaces. This relates Kashaev’s work with the theory of quantum Teichmüller space, which was developed by Chekhov–Fock, Kashaev and continued by Bonahon–Liu.

Keywords
quantum Teichmüller space, Kashaev's $6j$–symbol
Mathematical Subject Classification 2000
Primary: 57R56
Secondary: 20G42
References
Publication
Received: 23 July 2007
Accepted: 31 August 2007
Published: 14 November 2007
Authors
Hua Bai
Department of Mathematics
University of Georgia
Athens GA 30602
USA
http://www.math.uga.edu/~huabai/