Octonial like structures over arbitrary fields

A question occurred to me that I wonder if someone on this sub might be able to answer. Over R there are three extensions to larger algebras: C the complex numbers (a field extension), H the quaternions (the only nontrivial central simple algebra), and O the octonions (a central simple nonassociative algebra). Over other fields the central simple algebras are indexed by the second Galois cohomology of that field. Is there a similar gadget that over R gives the octonions (indexing central simple nonassociative algebras, or perhaps other objects if that is more appropriate).

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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs https://nevinmanimala.com

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