Mapping the geometry of the E6 group

In this paper, we present a construction for the compact form of the exceptional Lie group E-6 by exponentiating the corresponding Lie algebra e(6), which we realize as the sum of f(4), the derivations of the exceptional Jordan algebra J(3) of dimension 3 with octonionic entries, and the right multiplication by the elements of J(3) with vanishing trace. Our parametrization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E-6 via an F-4 subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for F-4. An interesting first application of these results lies in the fact that we are able to determine an explicit expression for the Haar invariant measure on the E-6 group manifold. (c) 2008 American Institute of Physics.