Cayley algebra

Cayley algebra

[′kā·lē ‚al·jə·brə]
(mathematics)
The nonassociative division algebra consisting of pairs of quaternions; it may be identified with an eight-dimensional vector space over the real numbers.
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These algebras form an interesting class of nonassociative, but almost associative up to a 3-cocycle, algebras including the well-known quaternions, octonions and higher Cayley algebras, see loc.