Maximal subgroups of the Coxeter group W(H4) and quaternions |
| |
Institution: | 1. Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Muscat, Oman;2. Department of Physics, Faculty of Engineering, Gaziantep University, 27310 Gaziantep, Turkey |
| |
Abstract: | The largest finite subgroup of O(4) is the non-crystallographic Coxeter group W(H4) of order 14,400. Its derived subgroup is the largest finite subgroup W(H4)/Z2 of SO(4) of order 7200. Moreover, up to conjugacy, it has five non-normal maximal subgroups of orders 144, two 240, 400 and 576. Two groups W(H2) × W(H2)] ⋊ Z4 and W(H3) × Z2 possess non-crystallographic structures with orders 400 and 240 respectively. The groups of orders 144, 240 and 576 are the extensions of the Weyl groups of the root systems of SU(3) × SU(3), SU(5) and SO(8) respectively. We represent the maximal subgroups of W(H4) with sets of quaternion pairs acting on the quaternionic root systems. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|