gh-35629: Implement the exceptional Jordan algebra

    
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### 📚 Description

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"The" exceptional Jordan algebra is a 27 dimensional algebra defined as
the $3 \times 3$ self-adjoint matrices over the octonions. This is an
important Jordan algebra as it is used to construct the simple Lie
group/algebra of type $F_4$.

Fixes #32940.

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### ⌛ Dependencies

- #35630 used in the construction

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URL: #35629
Reported by: Travis Scrimshaw
Reviewer(s): Frédéric Chapoton, Matthias Köppe, Travis Scrimshaw