Algebra A over field K with non-degenerate quadratic norm N: A → K satisfying N(xy) = N(x)N(y). Hurwitz theorem: dimensions 1, 2, 4, 8 only — ℝ, ℂ, ℍ, 𝕆 over ℝ. Cayley-Dickson construction generates each from previous.
Algebra A over field K with non-degenerate quadratic norm N: A → K satisfying N(xy) = N(x)N(y). Hurwitz theorem: dimensions 1, 2, 4, 8 only — ℝ, ℂ, ℍ, 𝕆 over ℝ. Cayley-Dickson construction generates each from previous.