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Introduction to Sporadic Groups
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Introduction to Sporadic Groups
Інший ID:
2010 Mathematics Subject Classification: 20D08; 20F99
DOI:10.3842/SIGMA.2011.009
DOI:10.3842/SIGMA.2011.009
Посилання:
Introduction to Sporadic Groups / L.J. Boya // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 34 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
Work supported by grant A/9335/07 of the PCI-AECI and grant 2007-E24/2 of DGIID-DGA. The author thanks Professors A. Andrianov (Barcelona) and L.M. Nieto (Valladolid) for the opportunity to present the material as a Seminar in the Conference on Supersymmetric Quantum Mechanics.
Дата:
2011
Переглядів:
490
Завантажень:
268
Анотація:
This is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. After a short review of group theory, we enumerate the 1+1+16=18 families of finite simple groups, as an introduction to the sporadic groups. These are described next, in three levels of increasing complexity, plus the six isolated ''pariah'' groups. The (old) five Mathieu groups make up the first, smallest order level. The seven groups related to the Leech lattice, including the three Conway groups, constitute the second level. The third and highest level contains the Monster group M, plus seven other related groups. Next a brief mention is made of the remaining six pariah groups, thus completing the 5+7+8+6=26 sporadic groups. The review ends up with a brief discussion of a few of physical applications of finite groups in physics, including a couple of recent examples which use sporadic groups.
