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Explicit Cayley triples in real forms of $$G_2$$, $$F_4$$, and $$E_6$$. (English) Zbl 1040.17004
Earlier the author classified nilpotent adjoint orbits of real simple noncompact groups [J. Algebra 112, 503–524 (1988; Zbl 0639.17005); J. Algebra 116, 196–207 (1988; Zbl 0653.17004)]. Here he classifies $$G_2, F_4,E_6$$ by giving explicit representatives for each orbit as linear combinations of vectors from a suitably normalized Chevalley basis of the complexified Lie algebra. Each representative is embedded in a Cayley triple; square roots in these coefficients are to be used.

##### MSC:
 17B20 Simple, semisimple, reductive (super)algebras 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
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