Comments on the classification of the finite subgroups of SU(3)

Autor(en)
Patrick Otto Ludl
Abstrakt

Many finite subgroups of SU(3) are commonly used in particle physics. The classification of the finite subgroups of SU(3) began with the work of H.F. Blichfeldt at the beginning of the 20th century. In Blichfeldt's work the two series (C) and (D) of finite subgroups of SU(3) are defined. While the group series Delta(3n^2) and Delta(6n^2) (which are subseries of (C) and (D), respectively) have been intensively studied, there is not much knowledge about the group series (C) and (D). In this work we will show that (C) and (D) have the structures (C) \cong (Z_m x Z_m') \rtimes Z_3 and (D) \cong (Z_n x Z_n') \rtimes S_3, respectively. Furthermore we will show that, while the (C)-groups can be interpreted as irreducible representations of Delta(3n^2), the (D)-groups can in general not be interpreted as irreducible representations of Delta(6n^2).

Organisation(en)
Teilchenphysik
Journal
Journal of Physics A: Mathematical and General
Band
44
Anzahl der Seiten
12
ISSN
0305-4470
DOI
https://doi.org/10.1088/1751-8113/44/25/255204
Publikationsdatum
2011
Peer-reviewed
Ja
ÖFOS 2012
103034 Teilchenphysik
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/comments-on-the-classification-of-the-finite-subgroups-of-su3(ed3a04be-5e7b-4d60-ad18-acaa341e5ac9).html