Comments about quantum symmetries of SU(3) graphs

R. Coquereaux (1, 2) , D. Hammaoui (3) , G. Schieber (1, 3, 4, 2) , E.H. Tahri (3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 LPTP - Laboratoire de Physique Théorique et des Particules
4 CBPF - Centro Brasileiro de Pesquisas Físicas

For the SU(3) system of graphs generalizing the ADE Dynkin digrams in the classification of modular invariant partition functions in CFT, we present a general collection of algebraic objects and relations that describe fusion properties and quantum symmetries associated with the corresponding Ocneanu quantum groupoïds. We also summarize the properties of the individual members of this system.

Mots clés: conformal field theory; modular invariance; Coxeter-Dynkin graphs; fusion algebra; quantum symmetries; quantum groupoïds

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Algèbres quantiques [math.QA]

R. Coquereaux, D. Hammaoui, G. Schieber, E.H. Tahri. Comments about quantum symmetries of SU(3) graphs. Journal of Geometry and Physics, 2006, 57 (1), pp.269-292. ⟨10.1016/j.geomphys.2006.03.002⟩. ⟨hal-00007739v2⟩