4 Aug
2005
4 Aug
'05
4 p.m.
me> Is there an interesting cubic extension of the octonians? various> Huh? dan> Please, folks: it's spelled "octonions". Obviously, by analogy with the Realions, Complexions, and Quaternions. We discussed the doubling process(es) before, giving systems with dimensiyn 8, 16, 32, etc. Is it possible to take a 3-step, going from octoniens to a system of dimensiun 24? There's be 24 unit elements, one of them the Real(ion)s, and various subsets isomorphic to the Cs, Qs, Octs. I'm imagining some relationship to the Monster group. Evidence against, is the absense of a degree 3 extensiin of R of this kind. Is this concluswve? Rich rcs@cs.arizona.edu