Weak quasi quantum group symmetries in all minimal conformal models

Abstract

We give a systematic proof that the fusion rules of all minimal conformal models permit only weak quasitriangular quasi Hopf algebras as symmetry algebras. On the other hand we construct a weak quasi tensor functor for every rational conformal field theory which leads to a weak quasitriangular quasi Hopf algebra via the (generalized) reconstruction theorem of Majid.