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Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation


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


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.

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Additional Metadata

Item Type: Article
Divisions: Institute for Mathematical Research
DOI Number: https://doi.org/10.3390/math5010006
Publisher: MDPI
Keywords: Finite groups; Dessins d’enfants; Finite geometries; Quantum commutation; Quantum contextuality
Depositing User: Mohd Hafiz Che Mahasan
Date Deposited: 30 Nov 2018 04:14
Last Modified: 30 Nov 2018 04:14
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/math5010006
URI: http://psasir.upm.edu.my/id/eprint/63744
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