From Orthocomplementations to Locality

After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal complementations to a one-to-one correspondence between a class...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2021
Hauptverfasser: Clavier, Pierre, Guo, Li, Paycha, Sylvie, Zhang, Bin
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2021
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211322
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:From Orthocomplementations to Locality. Pierre Clavier, Li Guo, Sylvie Paycha and Bin Zhang. SIGMA 17 (2021), 027, 23 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Clavier, Pierre
Guo, Li
Paycha, Sylvie
Zhang, Bin
author_facet Clavier, Pierre
Guo, Li
Paycha, Sylvie
Zhang, Bin
citation_txt From Orthocomplementations to Locality. Pierre Clavier, Li Guo, Sylvie Paycha and Bin Zhang. SIGMA 17 (2021), 027, 23 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal complementations to a one-to-one correspondence between a class of locality structures and orthocomplementations on bounded lattices. This recasts in the context of renormalisation classical results in lattice theory.
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issn 1815-0659
language English
last_indexed 2026-03-18T05:01:35Z
publishDate 2021
publisher Інститут математики НАН України
record_format dspace
spelling Clavier, Pierre
Guo, Li
Paycha, Sylvie
Zhang, Bin
2025-12-29T11:11:28Z
2021
From Orthocomplementations to Locality. Pierre Clavier, Li Guo, Sylvie Paycha and Bin Zhang. SIGMA 17 (2021), 027, 23 pages
1815-0659
2020 Mathematics Subject Classification: 06C15; 08A55; 81T15; 15A63
arXiv:2007.03003
https://nasplib.isofts.kiev.ua/handle/123456789/211322
https://doi.org/10.3842/SIGMA.2021.027
After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal complementations to a one-to-one correspondence between a class of locality structures and orthocomplementations on bounded lattices. This recasts in the context of renormalisation classical results in lattice theory.
This work is supported by the Natural Science Foundation of China (Grant Nos. 11771190, 11821001, 11890663). The first and third authors are grateful to the Perimeter Institute, where part of this paper was written. They also thank Tobias Fritz for inspiring discussions, and the third author is grateful to Daniel Bennequin for his very useful comments at a preliminary stage of the preparation of the paper. We greatly appreciate the very helpful suggestions of the referees on previous versions of the paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
From Orthocomplementations to Locality
Article
published earlier
spellingShingle From Orthocomplementations to Locality
Clavier, Pierre
Guo, Li
Paycha, Sylvie
Zhang, Bin
title From Orthocomplementations to Locality
title_full From Orthocomplementations to Locality
title_fullStr From Orthocomplementations to Locality
title_full_unstemmed From Orthocomplementations to Locality
title_short From Orthocomplementations to Locality
title_sort from orthocomplementations to locality
url https://nasplib.isofts.kiev.ua/handle/123456789/211322
work_keys_str_mv AT clavierpierre fromorthocomplementationstolocality
AT guoli fromorthocomplementationstolocality
AT paychasylvie fromorthocomplementationstolocality
AT zhangbin fromorthocomplementationstolocality