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

## Abstract

We describe the group Aut{sub br}¹(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 Out{sub 2₋cl}(G)⋉B(G) of the group of double class preserving automorphisms and the Bogomolov multiplier of G is a subgroup of Aut{sub br}¹(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{sup *}) of classes vanishing on abelian subgroups of G. We show that elements of Aut{sub br}¹(Z(G)) give rise to different realisations of the charge conjugation modular invariant for G-orbifolds of holomorphic conformal field theories.

- Authors:

- Department of Mathematics, Ohio University, Athens, Ohio 45701 (United States)

- Publication Date:

- OSTI Identifier:
- 22306038

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CONFORMAL GROUPS; CONFORMAL INVARIANCE; QUANTUM FIELD THEORY; TENSORS

### Citation Formats

```
Davydov, Alexei.
```*Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds*. United States: N. p., 2014.
Web. doi:10.1063/1.4895764.

```
Davydov, Alexei.
```*Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds*. United States. doi:10.1063/1.4895764.

```
Davydov, Alexei. Mon .
"Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds". United States.
doi:10.1063/1.4895764.
```

```
@article{osti_22306038,
```

title = {Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds},

author = {Davydov, Alexei},

abstractNote = {We describe the group Aut{sub br}¹(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 Out{sub 2₋cl}(G)⋉B(G) of the group of double class preserving automorphisms and the Bogomolov multiplier of G is a subgroup of Aut{sub br}¹(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{sup *}) of classes vanishing on abelian subgroups of G. We show that elements of Aut{sub br}¹(Z(G)) give rise to different realisations of the charge conjugation modular invariant for G-orbifolds of holomorphic conformal field theories.},

doi = {10.1063/1.4895764},

journal = {Journal of Mathematical Physics},

number = 9,

volume = 55,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}