Clifford Algebra 

Hi, I have't forgotten that you wanted to discuss a bit further. I'd like that too. I'm on sort of a semi-Wiki-break right now, but, in the meanwhile, could you elaborate on
By the way, I'm interested in seeing (if you have an example in mind) an illustrative example of leveraging basis elements of a complex space that square to -1. That sounds like an interesting benefit that might normally be passed over in pure math texts.
a bit. I'm not sure exactly what you mean, and there might be no mathematical significance, but there is surely physical significance to be extracted. The complexification is made partly for convenience, partly for the Clifford algebra to actually encompass the physicist convention for the Lie algebra, and partly to encompass transformations that come from , not . Actually, not even the full  suffices. In order to encompass time reversal, one must have the set of all antilinear transformations as well. These are constructed using complex conjugation and an ordinary complex linear transformation. Best!