Open Research Index

ehrlich-b/composition-algebras

Bryan Ehrlich

Palomar Registrypalomar/PALOMAR-2026-08-29-000018Aug 29, 2026math.RAscore 0

Hurwitz's theorem (1898), classification form: a nontrivial finite-dimensional Euclidean composition algebra over R - a unital, not necessarily associative or commutative bilinear product together with a symmetric positive-definite form whose quadratic form is multiplicative - is isomorphic to R, C, the quaternions or the octonions, by a linear isomorphism preserving the unit, the product and the norm form. All four targets are constructed, with Degen's eight-square identity discharging the octonion composition law, so every branch of the conclusion is attained. Machine checked, not peer…

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