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We re-examine the problem of classifying the nilpotent adjoint orbits in semisimple real Lie algebras. We present the list of representatives of these orbits, as well as those of related Cayley triples, in the case when the complexication of the algebra is one of the exceptional complex Lie algebras mentioned in the title.

Explicit Cayley triples in real forms of G2, F4, and E6

Explicit Cayley triples in real forms of G₂, F₄, and E₆