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 |
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| Date: | 2018 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| 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| _version_ | 1862660568471568384 |
|---|---|
| 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.
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| first_indexed | 2025-12-02T11:10:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209450 |
| 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 |