Dragomir Z. Dokovic
Explicit Cayley triples in real forms of E₇

Let g be a noncompact real form of the simple complex Lie algebra g^c of type E₇. Up to isomorphism, there are exactly three such algebras: EV, EVI, and EVII in Cartan notations. For each of these algebras we obtain a list of representatives of the adjoint orbits of standard triples (E, H, F), i.e., triples {E, H, F} \subset g spanning a subalgebra isomorphic to sl₂(R), and such that [H, E] = 2E, [H,F] = -2F, and [F, E] = H. These representative standard triples are chosen to be Cayley triples with respect to a fixed Cartan decomposition of g.