Tabla de Contenidos: “…-- 24 Complex quaternions and special relativity -- 24.1 Introducing 3 space and 1 time -- 24.2 Exploring complexified quaternions -- 24.3 Relativity from SL(2,C) and complexified quaternions -- 24.4 Four-vector Pauli matrices and the spacetime Lorentz group -- 24.5 Miscellaneous properties -- 24.6 Summary of (3 + 1)-dimensional relativity and complexified quaternions -- 8 Quaternion discrete symmetries and gravitons -- 25 Geometry of the ADE symmetries of the 2-sphere -- 25.1 Introduction to discrete groups on the sphere -- 25.2 Coordinates of the Ak cyclic geometry -- 25.3 Coordinates of the Dk dihedral geometry -- 25.4 Coordinates of the E6 tetrahedral geometry -- 25.5 Coordinates of the E7 octahedral geometry -- 25.6 Coordinates of the E8 icosahedral geometry -- 26 The discrete ADE rotation groups and their quaternions -- 26.1 Introduction -- 26.2 Actions of the SO(3) ADE rotations in Euclidean 3D space -- 26.3 Identifying the 3D symmetric ADE transformations -- 26.4 The quaternion actions of the Klein groups -- 26.4.1 The Ak cyclic quaternion group -- 26.4.2 The Dk dihedral quaternion group -- 26.4.3 The E6 tetrahedral quaternion group -- 26.4.4 The E7 octahedral quaternion group…”

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