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This category contains results about Octonions.
Definitions specific to this category can be found in Definitions/Octonions.

The set of octonions, usually denoted $\Bbb O$, can be defined by using the Cayley-Dickson construction from the quaternions $\Bbb H$ as follows:

From Quaternions form Algebra, $\Bbb H$ forms a nicely normed $*$-algebra.

Let $a, b \in \Bbb H$.

Then $\tuple {a, b} \in \Bbb O$, where:

$\tuple {a, b} \tuple {c, d} = \tuple {a c - d \overline b, \overline a d + c b}$
$\overline {\tuple {a, b} } = \tuple {\overline a, -b}$


$\overline a$ is the conjugate on $a$


$\overline {\tuple {a, b} }$ is the conjugation operation on $\Bbb O$.

Pages in category "Octonions"

The following 2 pages are in this category, out of 2 total.