Homomorphisms and Rigid Isomorphisms of Twisted Group Doubles

Abstract

We prove several results concerning quasi-bialgebra morphisms

Braid gaugings and categorical invariants

“…As a consequence, {p(e a )} a∈A is a basis of B. iii) [12,Theorem 3.15] Moreover, every element of A is equal to σ(•, b) for some unique b ∈ B, and every element of B is equal to σ(a, •) for some unique a ∈ A. iv) The set of all such p with A, B ⊆ Z(G) forms a group under the convolution product. This group is canonically isomorphic to Hom( Z(G), Z(G)), with the isomorphism given by the obvious restriction maps.…”

“…Next we recall a few of the basics about Rep(D(G)), which can be found in [7]. We adopt here the notation used in [12,Section 15] Suppose we are given a group G, s ∈ G, and a representation ρ of C G (s) on a finite dimensional -vector space V . Let class(s) = {s 0 = s, s 1 , .., s m }, denoted simply {s j }, be the conjugacy class of s in G.…”

“…By [16,Theorem 15.3] and its proof we have the following irreducible objects and corresponding data in Rep(D(G))…”