Octonions, triality, the exceptional Lie algebra F4 and polar actions on the Cayley hyperbolic plane
Octonions, triality, the exceptional Lie algebra F4 and polar actions on the Cayley hyperbolic plane
Using octonions and the triality property of Spin(8), we find explicit formulae for the Lie brackets of the exceptional simple real Lie algebras [Formula: see text] and [Formula: see text], i.e. the Lie algebras of the isometry groups of the Cayley projective plane and the Cayley hyperbolic plane. As an …