# Questions tagged [octonions]

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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### Exceptional symmetric spaces embedded in exceptional Lie group

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### $Spin(7)$ as stabilizer of a $4$-form

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### Is there an octonionic analog of the K3 surface, with implications for stable homotopy groups of spheres?

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### What finite simple groups we can obtain using octonions?

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### Atiyah on the “Galois group of the octonions” and Physics

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### Determinants of octonionic hermitian matrices

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