Implement the exceptional Jordan algebra

[tscrim]

📚 Description

"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.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

• Implement the octonions #35630 used in the construction

[fchapoton]

• missing the word "matrix" in the sentence self-adjoint 3x3 over an octonion

• do we have a category and a testsuite that checks the Jordan axioms ?

[tscrim]

• missing the word "matrix" in the sentence self-adjoint 3x3 over an octonion

Fixed.

• do we have a category and a testsuite that checks the Jordan axioms ?

There is no category as I feel the implementations are not complicated enough to warrant one (i.e., an ABC is sufficient). However, there was no _test_jordan_relations() method; I have added it. Good idea!

[fchapoton]

Thanks. The linter is slightly unhappy about too many blank lines.

[github-actions]

Documentation preview for this PR (built with commit 4772d05) is ready! 🎉

[tscrim]

The linter is now happy (to the extent it can be).

[fchapoton]

ok, thanks. Let's move on

[tscrim]

Thank you!