Quantum Teichmüller spaces and Kashaev’s 6j–symbols

Bai, Hua

doi:10.2140/agt.2007.7.1541

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Quantum Teichmüller spaces and Kashaev's $6j$–symbols

Hua Bai

Algebraic & Geometric Topology 7 (2007) 1541–1560

DOI: 10.2140/agt.2007.7.1541

Abstract

The Kashaev invariants of 3–manifolds are based on $6 j$ –symbols from the representation theory of the Weyl algebra, a Hopf algebra corresponding to the Borel subalgebra of $U_{q} (s l (2, ℂ))$ . In this paper, we show that Kashaev’s $6 j$ –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/

Volume 7, issue 3 (2007)