Quantum Dilogarithm as a 6j-Symbol
  The cyclic quantum dilogarithm is interpreted as a cyclic 6j-symbol of the Weyl algebra, considered as a Borel subalgebra $BU_q(sl(2))$. Using modified 6j-symbols, an invariant of triangulated links in triangulated 3-manifolds is constructed. Apparently, it is an ambient isotopy invariant of links. 
R. M. Kashaev