On Sat, Jul 28, 2018 at 3:31 PM, Mike Stay <metaweta@gmail.com> wrote:
On Sat, Jul 28, 2018 at 12:41 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Sedenions aren't a division algebra.
Octonions aren't associative. And your point is ...?
Furey isn't claiming that this is a Theory of Everything. She's just saying that if you take the Georgi–Glashow GUT, which uses SU(5), and then factor it as ℝ⊗ℂ⊗ℍ⊗𝕆 , which are the four normed division algebras,
SU(5) is a group (hence associative) of dimension 24 as a real manifold ( https://en.wikipedia.org/wiki/Special_unitary_group#Properties ) ℝ⊗ℂ⊗ℍ⊗𝕆 is a non-associative algebra over the reals of dimension 1*2*4*8= 64. So how can the latter be a factorization of the former? Clearly there is something else going on.