Categorical Tori

We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal Tori of simple and simply connected compact Lie groups and the Tori associated with the Leech and Niemeyer lattices. We o...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Author: Ganter, N.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209450
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Categorical Tori / N. Ganter // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 17 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Ganter, N.
author_facet Ganter, N.
citation_txt Categorical Tori / N. Ganter // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 17 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal Tori of simple and simply connected compact Lie groups and the Tori associated with the Leech and Niemeyer lattices. We obtain the extra-special 2-groups as the isomorphism classes of categorical fixed points under an involution action.
first_indexed 2025-12-02T11:10:55Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-02T11:10:55Z
publishDate 2018
publisher Інститут математики НАН України
record_format dspace
spelling Ganter, N.
2025-11-21T19:03:11Z
2018
Categorical Tori / N. Ganter // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 17 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 22E99; 18D99
arXiv:1406.7046
https://nasplib.isofts.kiev.ua/handle/123456789/209450
https://doi.org/10.3842/SIGMA.2018.014
We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal Tori of simple and simply connected compact Lie groups and the Tori associated with the Leech and Niemeyer lattices. We obtain the extra-special 2-groups as the isomorphism classes of categorical fixed points under an involution action.
The author was supported by an Australian Research Fellowship and by ARC grant DP1095815. It is a pleasure to thank David Roberts for very helpful conversations and correspondence, as well as his open referee report. The idea for Construction 2.1 came from a conversation with him, and I understand that he will also write about it elsewhere. I would like to thank Shan Shah for pointing out a mistake in an earlier version. Many thanks for helpful and inspiring conversations, also go to Matthew Ando, Konrad Waldorf, Thomas Nikolaus, Geoffrey Mason, Arun Ram, and Alex Ghitza. Finally, I wish to thank the anonymous referee for helpful comments.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Categorical Tori
Article
published earlier
spellingShingle Categorical Tori
Ganter, N.
title Categorical Tori
title_full Categorical Tori
title_fullStr Categorical Tori
title_full_unstemmed Categorical Tori
title_short Categorical Tori
title_sort categorical tori
url https://nasplib.isofts.kiev.ua/handle/123456789/209450
work_keys_str_mv AT gantern categoricaltori