Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation
Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfa...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI
2017
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/63744/ http://psasir.upm.edu.my/id/eprint/63744/1/Zoology%20of%20Atlas-Groups%20Dessins%20D%E2%80%99enfants%2C.pdf |
| _version_ | 1848854859160223744 |
|---|---|
| author | Planat, Miche Zainuddin, Hishamuddin |
| author_facet | Planat, Miche Zainuddin, Hishamuddin |
| author_sort | Planat, Miche |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfant D and that most standard graphs and finite geometries G - such as near polygons and their generalizations -are stabilized by a D. In our paper, tripods P − D − G of rank larger than two,corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G′s have a contextuality parameter close to its maximal value 1. |
| first_indexed | 2025-11-15T11:16:33Z |
| format | Article |
| id | upm-63744 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:16:33Z |
| publishDate | 2017 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-637442018-11-30T04:14:34Z http://psasir.upm.edu.my/id/eprint/63744/ Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation Planat, Miche Zainuddin, Hishamuddin Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfant D and that most standard graphs and finite geometries G - such as near polygons and their generalizations -are stabilized by a D. In our paper, tripods P − D − G of rank larger than two,corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G′s have a contextuality parameter close to its maximal value 1. MDPI 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/63744/1/Zoology%20of%20Atlas-Groups%20Dessins%20D%E2%80%99enfants%2C.pdf Planat, Miche and Zainuddin, Hishamuddin (2017) Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation. Mathematics, 5 (1). p. 43117. ISSN 2227-7390 10.3390/math5010006 |
| spellingShingle | Planat, Miche Zainuddin, Hishamuddin Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation |
| title | Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation |
| title_full | Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation |
| title_fullStr | Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation |
| title_full_unstemmed | Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation |
| title_short | Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation |
| title_sort | zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation |
| url | http://psasir.upm.edu.my/id/eprint/63744/ http://psasir.upm.edu.my/id/eprint/63744/ http://psasir.upm.edu.my/id/eprint/63744/1/Zoology%20of%20Atlas-Groups%20Dessins%20D%E2%80%99enfants%2C.pdf |