Quasitriangular structures of the double of a finite group

摘要

We give a classification of all quasitriangular structures and ribbon elements of MATHEMATICAL SCRIPT CAPITAL D(G) explicitly in terms of group homomorphisms and central subgroups. This can equivalently be interpreted as an explicit description of all braidings with which the tensor category Rep(MATHEMATICAL SCRIPT CAPITAL D(G)) can be endowed. We also characterize their equivalence classes under the action of Aut(MATHEMATICAL SCRIPT CAPITAL D(G)) and determine when they are factorizable.