Bogomolov multiplier, double class-preserving automorphisms and modular invariants for orbifolds

Abstract

We describe the group of braided tensor autoequivalences of the Drinfeld centre of a finite group $G$ isomorphic to the identity functor (just as a functor) as a semi-direct product $Au{t}_{br}^1(\mathbb{Z}(G))\simeq Ou{t}_{2-cl}(G)⋉B(G)$ of the group of double class preserving automorphisms and the Bogomolov multiplier of $G$. The Bogomolov multiplier $B(G)$ is the subgroup of its Schur multiplier $H^2(G,k^{\ast })$ of classes vanishing on abelian subgroups of $G$. We show that elements of $Au{t}_{br}^1(\mathbb{Z}(G))$ give rise to different realisations of the charge conjugation modular invariant for $G$-orbifolds of holomorphic conformal field theories.

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References in corpus (1)

• Categorification and correlation functions in conformal field theory

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