Racah–Wigner quantum 6J6J symbols, Ocneanu cells for ANAN diagrams and quantum groupoids

We relate quantum 6J6J symbols of various types (quantum versions of Wigner and Racah symbols) to Ocneanu cells associated with ANAN Dynkin diagrams. We check explicitly the algebraic structure of the associated quantum groupoids and analyze several examples. Some features relative to cells associated with more general ADE diagrams are also discussed.