Re: Lie group F4 = Aut(OP2)

Indeed (non-)associativity spoils the conventional
technique of using
equivalence classes of scale invariant coordinates to
construct OP².
Instead one defines OP² using the exceptional Jordan
algebra J(3,O),
where points of OP² consist of those matrices of
J(3,O) with vanishing
Freudenthal product (A x A = 0).
(...)

Thank you for this answer. However it is not enough for me. This definition is not intuitive enough, not geometrical enough for me. I would like to imagine how the OP2 looks.
Do you know any analogy of the Jordan algebra and OP2 to quaternions ?

I don't have enough time to investigate how the non-associativity spoil the octonionic planes in O2 and O3.
Let (x,y) belong to O2. Define plane [x,y] as the one generated by vectors (x,y), (e1x,e1y),...(e7x,e7y) where e1...e7 are base octonion. The problem is whether (e2e1x, e2e1y) belongs to [x,y] ? I would like to see example when it doesn't.

Regards,
M.M.

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