10 Mar
2015
10 Mar
'15
10:16 a.m.
Think of R^4 as chopped into cubes of side = 1/2, each corresponding to the quaternion at its (+,+,+,+) vertex. Every unit cube in 4-space is 16 of these side-(1/2) cubes, so has 16 of these (+,+,+,+) vertices. The Hurwitz quaternions correspond to 2 of these vertices, and the Lipschitz quaternions to just 1 of them. So it would appear that the index is 2. --Dan
On Mar 10, 2015, at 8:38 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
https://en.wikipedia.org/wiki/Hurwitz_quaternion
<< The Lipschitz quaternions L form an index 2 sublattice of H. >>
"index 3" , I think ?! See eg. Conway & Smith sect. 5.5 .