Global Symmetries, Local Symmetries and Groupoids
Local symmetries are primarily defined in the case of spacetime, but several authors have defined them outside this context, sometimes with the help of groupoids. We show that, in many cases, local symmetries can be defined as global symmetries. We also show that groups can be used, rather than grou...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/10/1905 |
| _version_ | 1797513085054877696 |
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| author | Michel Petitjean |
| author_facet | Michel Petitjean |
| author_sort | Michel Petitjean |
| collection | DOAJ |
| description | Local symmetries are primarily defined in the case of spacetime, but several authors have defined them outside this context, sometimes with the help of groupoids. We show that, in many cases, local symmetries can be defined as global symmetries. We also show that groups can be used, rather than groupoids, to handle local symmetries. Examples are given for graphs and networks, color symmetry and tilings. The definition of local symmetry in physics is also discussed. |
| first_indexed | 2024-03-10T06:10:43Z |
| format | Article |
| id | doaj.art-b1c13f7aa74f4023a4523406f993e9a5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T06:10:43Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b1c13f7aa74f4023a4523406f993e9a52023-11-22T20:10:51ZengMDPI AGSymmetry2073-89942021-10-011310190510.3390/sym13101905Global Symmetries, Local Symmetries and GroupoidsMichel Petitjean0BFA, CNRS UMR 8251, INSERM ERL U1133, Université de Paris, 75013 Paris, FranceLocal symmetries are primarily defined in the case of spacetime, but several authors have defined them outside this context, sometimes with the help of groupoids. We show that, in many cases, local symmetries can be defined as global symmetries. We also show that groups can be used, rather than groupoids, to handle local symmetries. Examples are given for graphs and networks, color symmetry and tilings. The definition of local symmetry in physics is also discussed.https://www.mdpi.com/2073-8994/13/10/1905global symmetrylocal symmetrygroupoids |
| spellingShingle | Michel Petitjean Global Symmetries, Local Symmetries and Groupoids Symmetry global symmetry local symmetry groupoids |
| title | Global Symmetries, Local Symmetries and Groupoids |
| title_full | Global Symmetries, Local Symmetries and Groupoids |
| title_fullStr | Global Symmetries, Local Symmetries and Groupoids |
| title_full_unstemmed | Global Symmetries, Local Symmetries and Groupoids |
| title_short | Global Symmetries, Local Symmetries and Groupoids |
| title_sort | global symmetries local symmetries and groupoids |
| topic | global symmetry local symmetry groupoids |
| url | https://www.mdpi.com/2073-8994/13/10/1905 |
| work_keys_str_mv | AT michelpetitjean globalsymmetrieslocalsymmetriesandgroupoids |