4 ms·
Why stop at octonions? Sedenions and other steps of Cayley-Dickson construction?..
by avmich 6y ago
Why stop at octonions? Sedenions and other steps of Cayley-Dickson construction?..
- surfsvammel 6y agoIf I read the article correctly, it would seem its not needed.
- zamalek 6y agoDue to Hurwitz's theorem, as-per the article.
- avmich 6y agoFrom https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_constru... - "The Hurwitz's theorem (composition algebras) states that the reals, complex numbers, quaternions, and octonions are the only (normed) division algebras (over the real numbers)." So what? From https://en.wikipedia.org/wiki/Sedenion https://en.wikipedia.org/wiki/Sedenion - "Every sedenion is a linear combination of the unit sedenions e_0...e_15 , which form a basis of the vector space of sedenions." - clearly we still have operations to work with. Stopping at octonions looks somewhat arbitrary.