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Results tagged with octonions
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user 106010
Octonions form a 8-dimensional normed division algebra constructed over the reals. They can be seen as a non-associative (alternative) extension of the quaternions. They have been first defined and studied in the 19th century by John Graves and Arthur Cayley. There are several variants (such as split-octonions) and strong relations with Lie Groups and projective geometry.
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Are two octonion algebras with different multiplications isomorphic?
Baez, Ward, defined multiplication of octonions by formula
$
(a,b) \cdot^B (c,d)=(ac-db^*, cb+a^*d) \textrm{ for } a,b,c,d\in \mathbb H,
$
some others, e.g. Springer & Veldkamp, N. …
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