{"id":"palomar/PALOMAR-2026-08-29-000018","url":"https://github.com/ehrlich-b/composition-algebras/tree/98d4437ce1bfd8d042b8383e0cfe28ec3e595eee","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-29-000018-v1.json","repo":"https://github.com/ehrlich-b/composition-algebras","tags":["math.RA","math.RT","msc:17A75","msc:11E88","msc:17A35","msc:17D05","msc:17C40","msc:15A63","composition-algebras","hurwitz-theorem"],"score":0,"title":"ehrlich-b/composition-algebras","trust":"high","domain":"math.RA","source":"palomar","authors":["Bryan Ehrlich"],"reviews":0,"subject":"math.RA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-29","reactions":{},"formalized":true,"formalizes":[{"title":"Uber die Composition der quadratischen Formen von beliebig vielen Variablen","identifier":"","relationship":"adapts"},{"title":"Composition algebras and their applications, and the nucleus of an alternative algebra","identifier":"","relationship":"formalizes"}]}