Modular Categories and Hopf Algebras

The modularity of a ribbon Hopf algebra is characterized by the Drinfeld map. An elementary approach to Etingof and Gelakiʹs (1998, Math. Res. Lett.5, 119–-197) result on the dimensions of irreducible modules is given by deducing the necessary identities involving the matrix (Sij) from the well-known orthogonal relations of Hopf algebra characters.