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The Geometry of the Octonions

The Geometry of the Octonions is a mathematics book on the octonions, a system of numbers generalizing the complex numbers and quaternions, presenting its material at a level suitable for undergraduat

Bioctonion

In mathematics, a bioctonion, or complex octonion, is a pair (p,q) where p and q are biquaternions. The product of two bioctonions is defined using biquaternion multiplication and the biconjugate p →

G2 (mathematics)

In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras as well as some algebraic groups. They are the smallest of the

Octonion

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface O

Seven-dimensional cross product

In mathematics, the seven-dimensional cross product is a bilinear operation on vectors in seven-dimensional Euclidean space. It assigns to any two vectors a, b in a vector a × b also in . Like the cro

Octonion algebra

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 a unital non-associative algebra A over F with a

Split-octonion

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

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