• 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
  • Thumbnail for Grand Unified Theory
    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
  • 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 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
  • 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
  • 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
  • 8
    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
  • Thumbnail for SO(8)
    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