Explicit Cayley triples in real forms of E₈

Vol. 194 (2000), No. 1, 57–82

DOI: 10.2140/pjm.2000.194.57

Abstract

Let g be a noncompact real form of the simple complex Lie algebra g^c of type E₈. We obtain a list of representatives of the adjoint orbits of triples {E,H,F}⊂ g, spanning a subalgebra isomorphic to ₂(R), such that [H,E] = 2E, [H,F] = −2F, and [F,E] = H. They are chosen to be Cayley triples with respect to a fixed Cartan decomposition of g.

Milestones

Received: 19 May 1998

Published: 1 May 2000