On 12/15/09, Fred lunnon <fred.lunnon@gmail.com> wrote:
... First instalment is a skeletal summary introducing
1. Clifford Algebras ____________________ ...
Andy has queried how quaternions fit into this framework. Unfortunately, quaternions could be modelled by the Clifford algebra Cl(0,2); but it's a very bad idea because their symmetry is then lost. A much better model is the even subalgebra of the complex biquaternions Cl(3,0): with generators \x,\y,\z, we have i = \z\y, j = \x\z, k = \y\x. Note that these are bivectors (grade 2), representing rotations in space --- as opposed to vectors (grade 1), which generally represent prime reflections (that is, in "hyperplanes"). This confusion over quaternions is just one of many traps for the unwary ... Fred