Physics – High Energy Physics – High Energy Physics - Theory

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2005-10-22

Linear Algebra Appl. 412 (2006) 441-452

Physics

High Energy Physics

High Energy Physics - Theory

Linear Algebra and Its App. To be published

Scientific paper

The largest finite subgroup of O(4) is the noncrystallographic Coxeter group $W(H_{4})$ of order 14400. Its derived subgroup is the largest finite subgroup $W(H_{4})/Z_{2}$ 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 $[ W(H_{2})\times W(H_{2})] \times Z_{4}$ and $W(H_{3})\times Z_{2}$ possess noncrystallographic 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 $SU(3)\times SU(3)$%, SU(5) and SO(8) respectively. We represent the maximal subgroups of $% W(H_{4})$ with sets of quaternion pairs acting on the quaternionic root systems.

**Al-Barwani Muataz**

Physics – Condensed Matter – Mesoscale and Nanoscale Physics

Scientist

**Al-Farsi Shadia**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Koc Ramazan**

Physics – Mathematical Physics

Scientist

**Koca Mehmet**

Physics – Mathematical Physics

Scientist

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