A 2-group construction from an extension of the 3-loop group \(\varOmega ^3G\)
type: Item
instance of: scholarly article
title: A 2-group construction from an extension of the 3-loop group \(\varOmega ^3G\)
zbMATH Open document ID: 1430.22027
author: Ossi Niemimäki
author: Jouko Mickelsson
published in: Letters in Mathematical Physics
publication date: 2019-11-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1810.00230
review text: Let \(G\) be a Lie group. The paper under review studies the \(3\)-loop group \(\Omega^3 G\) of based maps from the \(3\)-sphere to \(G\). It turns out that the related Mickelsson-Faddeev cocycle depends crucially on the defining Lie algebra valued \(1\)-forms over the domain and, in particular, the corresponding Lie group extension is not central. The Mickelsson-Faddeev extension of \(\Omega^3 G\) admits an action of a certain extension of the group of all smooth maps from a \(3\)-ball to \(G\) which are flattened on the boundary. This is used to construct a strict \(2\)-group associated to the Mickelsson-Faddeev extension of \(\Omega^3 G\).
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 22E67
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 7138300
zbMATH Keywords: loop group
zbMATH Keywords: Lie 2-group
zbMATH Keywords: Mickelsson-Faddeev extension
MaRDI profile type: Publication
OpenAlex ID: W3098361592
arXiv ID: 1810.00230
cites work: Q3156490
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DOI: 10.1007/S11005-019-01201-Y
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description: scientific article