Quaternionic Roots of E 8 Related Coxeter Graphs and Quasicrystals

Authors : Mehmet KOCA, Nazife Özdeş KOCA

Pages : 421-436

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :The lattice matching of two sets of quaternionic roots of F4 leads to quaternionic roots of E8 which has a decomposition H4 + s 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 + s H3 describing the root system of the Lie algebra D6. It is noted that there exist three lattices in 6-dimensions whose point group Winsert ignore into journalissuearticles values(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 Winsert ignore into journalissuearticles values(A4); where H2 + s H2 constitute the root system of the Lie algebra A4. The relevance of these systems to quasicrystals are discussed.
Keywords : Turk J Phys, 22, 1998, 421 436 Turk J Phys, vol 22, iss 5