Quantum Teichmüller spaces and Kashaev's 6j-symbols

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 $U_q(sl(2,\C))$. 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.

18 pages, 2 figures

References in corpus (2)

• A Link Invariant from Quantum Dilogarithm
• Quantum Hyperbolic State Sum Invariants of 3-Manifolds

Cited by in corpus (6)

• Local representations of the quantum Teichmuller space
• Analytic families of quantum hyperbolic invariants
• Quantum holonomic link invariants derived from stated skein algebras
• Finite dimensional quantum Teichmüller space from the quantum torus at root of unity
• Quantum coadjoint action and the $6j$-symbols of $U_{q}s{l}_2$
• A survey of quantum Teichmüller space and Kashaev algebra