Alternative algebra & octonions

Algebra A satisfies x(xy) = x²y and (yx)x = yx² (alternativity, weaker than associativity). Hurwitz: only normed division algebras over ℝ are ℝ, ℂ, ℍ (quaternions), 𝕆 (octonions). Octonions are 8-dim, non-associative; underlie…