Title: Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds
Abstract: We describe the group $Aut_{br}^1({\cal Z}(G))$Autbr1(Z(G)) of braided tensor autoequivalences of the Drinfeld centre of a finite group G isomorphic to the identity functor (just as a functor). We prove that the semi-direct product Out2 − cl(G)⋉B(G) of the group of double class preserving automorphisms and the Bogomolov multiplier of G is a subgroup of $Aut_{br}^1({\cal Z}(G))$Autbr1(Z(G)). An automorphism of G is double class preserving if it preserves conjugacy classes of pairs of commuting elements in G. The Bogomolov multiplier B(G) is the subgroup of its Schur multiplier H2(G, k*) of classes vanishing on abelian subgroups of G. We show that elements of $Aut^1_{br}({\cal Z}(G))$Autbr1(Z(G)) give rise to different realisations of the charge conjugation modular invariant for G-orbifolds of holomorphic conformal field theories.