Abstract (Elsevier)
We show how spinors in space-times of dimension D = t + s , where t is the time dimension, are associated for s - t = 1, 2, 4, 8 (and if t = 0, 1, 2) with the number systems (division algebras), |R, C, H, O . For t = 1 and s - t = 1, 2, 4 this association is “realized” by the sequence of Lorentz groups S1(2, |R ), S1(2; |C ), S1(2; |H ) for D = 3, 4, 6 respectively. We discuss how octonions may be related to D = 10. For D = 6 we give details of S1(2; |H ) spinors and construct supersymmetric models with them. These results explain various “empirical” observations in the literature relating quaternions and supersymmetry.