Dilogarithme Quantique et 6j-Symboles Cycliques

الأصل · EN

Let Wₙ be a quantized Borel subalgebra of Uq(sl(2,)), specialized at a primitive root of unity ω= (2iπ/N) of odd order N >1. One shows that the 6j-symbols of cyclic representations of Wₙ are representations of the canonical element of a certain extension of the Heisenberg double of Wₙ. 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.