Next Article in Journal
Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity
Previous Article in Journal
Logical Entropy of Dynamical Systems—A General Model
Article Menu

Export Article

Open AccessArticle
Mathematics 2017, 5(1), 6; doi:10.3390/math5010006

Zoology of Atlas-Groups: Dessins D’enfants, Finite Geometries and Quantum Commutation

1
Institut FEMTO-ST, CNRS, 15 B Avenue des Montboucons, F-25033 Besançon, France
2
Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Malaysia
*
Author to whom correspondence should be addressed.
Academic Editor: Indranil SenGupta
Received: 19 September 2016 / Revised: 12 December 2016 / Accepted: 5 January 2017 / Published: 14 January 2017
View Full-Text   |   Download PDF [469 KB, uploaded 14 January 2017]   |  

Abstract

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 necessarily minimal) permutation representations P . It is unusual, but significant to recognize that a P is a Grothendieck’s “dessin d’enfant” D and that a wealth of 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 of the defined geometries G s have a contextuality parameter close to its maximal value of one. View Full-Text
Keywords: finite groups; dessins d’enfants; finite geometries; quantum commutation; quantum contextuality finite groups; dessins d’enfants; finite geometries; quantum commutation; quantum contextuality
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Planat, M.; Zainuddin, H. Zoology of Atlas-Groups: Dessins D’enfants, Finite Geometries and Quantum Commutation. Mathematics 2017, 5, 6.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top