chapter  16
11 Pages

The automorphism group of C4: C. W. Kilmister

One of the most pressing mathematical problems thrown up by the highly original work of David Bohm 1 is to construct numerous detailed examples that will help in the understanding of the important concepts of implicate and explicate order. Recently Bohm and Hiley2 have themselves stressed the important role played by the Clifford algebras Cn here, since the automorphisms of the (even) Clifford algebras C2r are all inner and 'any theory based on an algebra can always be put in an implicate order by an inner automorphism of the algebra'3. To make the notation precise, I am using Cn for the algebra generated by n anticommuting elements, which I usually denote by Ei(i = 1 ... n), but in the case of quaternions, C2 , I use e 1, e2 , and set e3 = e 1e2 • Thus Cn has a basis of2n elements, including the unit, which I call 1. Unless explicitly stated otherwise, the algebra is over the field of reals, R.