Open Research Index

ehrlich-b/composition-algebras

Bryan Ehrlich

Palomar Registrypalomar/PALOMAR-2026-08-29-000015Aug 29, 2026math.RAscore 0

Hurwitz's theorem (1898), dimension 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 - has real dimension 1, 2, 4 or 8. R, C and H are exhibited so the class is inhabited; the classification into R, C, H and O is strictly stronger and is not part of this entry. Machine checked, not peer reviewed, no priority claim.

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