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 |
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| Datum: | 2021 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| 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| _version_ | 1862694802322096128 |
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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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| first_indexed | 2026-03-18T05:01:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211322 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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 |