I demand that Robert G. Brown are belonging when Thu, May 11, 2006 at 10:00:10PM -0400: > > That's why I am hesitant about seeing quaternions done out of context, > as it were. If anybody ever does decide to do a real Clifford/Geometric > algebra package with the grade (dimension) of the algebra basically a > free input parameter, it would both include quaternions as a particular > grade and would probably represent them slightly differently. Of course > the same could be said about complex.
There is one other narrow area where quaternions and octonians (together with real and complex) enjoy a "special" place in the grand scheme of things, and that is in the Berger classification of Riemann symetric spaces (see wikipedia entries on "holonomy" and "Calabi-Yau manifold"). Basically, if a space is symmetric, its going to be a product of real or complex or quaternion or octonian thise SO(n) or SU(n) or Sp(n) or the special cases of G_2 or Spin(7)). But again, this is "obscure" and would not be an argument for inclusion in GSL. The point is only that quaternions are in a certain way "special" and in a certain way a "natural" extension of the complex numbers in a way that general clifford algebras are not. --linas
