mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented...
39 KB (4,767 words) - 18:42, 8 October 2024
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...
7 KB (818 words) - 08:14, 5 January 2024
mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers. Unlike the standard octonions, they contain non-zero...
12 KB (1,669 words) - 22:44, 1 September 2024
Grand Unified Theory (section Octonion representations)
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...
35 KB (4,567 words) - 00:10, 7 October 2024
Okubo algebra (redirect from Pseudo-octonion algebra)
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...
7 KB (830 words) - 15:50, 21 February 2024
Cayley plane (redirect from Octonion projective plane)
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...
4 KB (412 words) - 18:21, 23 July 2024
Cayley–Dickson construction (section Octonions)
Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition algebras frequently applied in...
18 KB (2,272 words) - 11:16, 8 October 2024
E8 lattice (section Integral octonions)
real octonions O. It is possible to define the concept of an integral octonion analogous to that of an integral quaternion. The integral octonions naturally...
22 KB (3,560 words) - 15:51, 1 October 2024
triangular faces, whose first stellation is the cube-octahedron compound. The octonions are a hypercomplex normed division algebra that are an extension of the...
62 KB (6,371 words) - 18:35, 26 September 2024
SO(8) (section Unit octonions)
bimultiplications by unit octonions (a bimultiplication being the composition of a left-multiplication and a right-multiplication by the same octonion and is unambiguously...
7 KB (1,090 words) - 18:50, 9 February 2022