--- Richard Schroeppel <rcs@CS.Arizona.EDU> wrote:
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
Once you no longer require the algebra to be a division algebra, they become much easier to construct. If e[j], j=1..n is a basis for the linear space, arbitrarily choose coefficients c[ijk] in the ground field, and define e[i] e[j] = sum(c[ijk] e[k], k=1..n). Every finite dimensional algebra is of this form. Gene __________________________________ Do you Yahoo!? Yahoo! Mail - Find what you need with new enhanced search. http://info.mail.yahoo.com/mail_250