Quaternionic root systems and subgroups of the Aut(F4)

摘要: Cayley-Dickson doubling procedure is used to construct the root systems of some celebrated Lie algebras in terms integer elements division real numbers, complex quaternions, and octonions. Starting with roots weights SU(2) expressed as numbers one can SO(4),SP(2)≈SO(5),SO(8),SO(9),F4 E8 discrete algebras. The themselves display groups structures besides octonionic which form a closed octonion algebra. automorphism group Aut(F4) Dynkin diagram F4 order 2304, largest crystallographic four-dimensional Euclidean space, realized direct product two binary octahedral quaternions preserving quaternionic system F4. Weyl many algebras, such as, G2,SO(7),SO(8),SO(9),SU(3)XSU(3), SP(3)×SU(2) have been constructed subgroups Aut(F4). We also class...