mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented...

In mathematics, an octonion algebra or Cayley algebra over a field F is a composition algebra over F that has dimension 8 over F. In other words, it is...

mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers. Unlike the standard octonions, they contain non-zero...

Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition algebras frequently applied in...

the octonions. The Cayley plane was discovered in 1933 by Ruth Moufang, and is named after Arthur Cayley for his 1845 paper describing the octonions. In...

The Geometry of the Octonions is a mathematics book on the octonions, a system of numbers generalizing the complex numbers and quaternions, presenting...

In algebra, an Okubo algebra or pseudo-octonion algebra is an 8-dimensional non-associative algebra similar to the one studied by Susumu Okubo. Okubo algebras...

Petrie polygon of the tesseract and the 16-cell is a regular octagon. The octonions are a hypercomplex normed division algebra that are an extension of the...

generation of 16 fermions can be put into the form of an octonion with each element of the octonion being an 8-vector. If the 3 generations are then put in...

bimultiplications by unit octonions (a bimultiplication being the composition of a left-multiplication and a right-multiplication by the same octonion and is unambiguously...