“…The symmetry of the form L(v 27 ) = 1, that is the symmetry leaving det(X ) invariant, is a real form of E 6 as we briefly review here. We closely follow references [4,5,6,7,8] within which, in particular, the means of accommodating, and employing, the non-associative property of the octonions is described in detail. As a generalisation from the SL(2, C) ≡ Spin + (1, 3) Lorentz transformations of equation 19 a set of 2 × 2 matrix actions with M ∈ SL(2, O) ≡ Spin + (1, 9) can be embedded in the upper-left corner of 3 × 3 matrices M to obtain a conjugation action for the 3 × 3 case R : X → MX M † with:…”