ملخص
The lattice matching of two sets of quaternionic roots of F4 leads to quaternionic roots of E8 which has a decomposition H4 + σ H4 where the Coxeter graph H4 is represented by the 120 quaternionic elements of the binary icosahedral group. The 30 pure imaginary quaternions constitute the roots of H3 which has a natural extension to H3 + σ H3 describing the root system of the Lie algebra D6. It is noted that there exist three lattices in 6-dimensions whose point group W(D6) admits the icosahedral symmetry H3 as a subgroup, the roots of which describe the mid-points of the edges of an icosahedron. A natural extension of the Coxeter group H2 of order 10 is the Weyl group W(A4) where H2 + σ H2 constitute the root system of the Lie algebra A4. The relevance of these systems to quasicrystals are discussed.
اللغة الأصلية | English |
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الصفحات (من إلى) | 421-435 |
عدد الصفحات | 15 |
دورية | Turkish Journal of Physics |
مستوى الصوت | 22 |
رقم الإصدار | 5 |
حالة النشر | Published - 1998 |
ASJC Scopus subject areas
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