Explicit Cayley triples in real forms of E₇

Dragomir Ž. Ðoković

Vol. 191 (1999), No. 1, 1–23

DOI: 10.2140/pjm.1999.191.1

Abstract

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}⊂ g spanning a subalgebra isomorphic to ₂(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.

Milestones

Received: 14 January 1998

Revised: 24 April 1998

Published: 1 November 1999