Dilogarithme Quantique et 6j-Symboles Cycliques

Details Dilogarithme Quantique et 6j-Symboles Cycliques Dilogarithme Quantique et 6j-Symboles Cycliques

2002-02-26

arxiv.org/abs/math/0202272v1

Mathematics

Quantum Algebra

40 pages, in French (abstract in English). Former 3rd chapter of the Author's PhD thesis

Scientific paper

Let $\mathcal{W}_N$ be a quantized Borel subalgebra of $U_q(sl(2,\mc))$, specialized at a primitive root of unity $\omega = \exp(2i\pi/N)$ of odd order $N >1$. One shows that the $6j$-symbols of cyclic representations of $\mathcal{W}_N$ are representations of the canonical element of a certain extension of the Heisenberg double of $\mathcal{W}_N$. This canonical element is a twisted $q$-dilogarithm. In particular, one gives explicit formulas for these $6j$-symbols, and one constructs partial symmetrizations of them, the c-$6j$-symboles. The latters are at the basis of the construction of the quantum hyperbolic invariants of 3-manifolds.

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