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Title: 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:
 [1]
  1. 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}
}