See Conway & Sloane, pp.52--55 and 118--119. R. On Wed, 11 Mar 2015, Andy Latto wrote:
I'm not sure how you're multiplying 4-vectors. If you're multiplying them componentwise,
(root2/2, root2/2,0,0) ^2 = (1/2, 1/2, 0, 0).
If you're multiplying them as quaternions,
roott2/2 + root2/2 * i = i
So I can't tell in what sense the set of points you give is a multiplicative system.
Andy
On Wed, Mar 11, 2015 at 4:32 PM, Dan Asimov <asimov@msri.org> wrote:
It appears to me that the 24 points on the unit sphere S^3 in R^4, of form
(±√½, ±√½, 0, 0) (and permutations)
form a multiplicative system with inverses.
QUESTION:
How many such 24-element multiplicative systems with inverses are there in S^3 ?
--Dan
On Mar 10, 2015, at 9:11 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
. . . the fact that the Lipschitz quaternions of unit norm (abstractly Q_8) form an index-3 normal subgroup of the Hurwitz quaternions of unit norm (abstractly 2T):
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