Bogomolov multiplier, double classpreserving 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 semidirect 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 Gorbifolds 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 classpreserving automorphisms, and modular invariants for orbifolds. United States: N. p., 2014.
Web. doi:10.1063/1.4895764.
Davydov, Alexei. Bogomolov multiplier, double classpreserving automorphisms, and modular invariants for orbifolds. United States. doi:10.1063/1.4895764.
Davydov, Alexei. Mon .
"Bogomolov multiplier, double classpreserving automorphisms, and modular invariants for orbifolds". United States.
doi:10.1063/1.4895764.
@article{osti_22306038,
title = {Bogomolov multiplier, double classpreserving 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 semidirect 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 Gorbifolds 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}
}

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