nostr:nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqgyewnrnvhqg0dlqmn5mfp0wjcvpkgxycjat9527w8cmf0c6cxwqs9njev0 - "Are these descriptions equivalent?" You have to take the theorem below as definitive, not any of these simple-sounding verbal descriptions.

For example, to say "that preserve a choice of ℂ⊂𝕆" or "we take those symmetries which preserve a ℂ⊂𝕆" is sloppy. We're starting with automorphisms of 𝔥₃(𝕆) and finding a subgroup of those. But an automorphism of 𝔥₃(𝕆) does not act on 𝕆!

What does make sense is for an automorphism of 𝔥₃(𝕆) to preserve a Jordan subalgebra isomorphic to 𝔥₃(ℂ).

That's what I was saying, in abbreviated form, on the slide: "choose a subalgebra 𝔥₃(ℂ) ⊂ 𝔥₃(𝕆)" is my abbreviated way of saying "choose a Jordan subalgebra of 𝔥₃(𝕆) isomorphic to 𝔥₃(ℂ)."

I need to write a paper, simply to clarify all this.