  In this paper we present a construction for the compact form of the
exceptional Lie group E6 by exponentiating the corresponding Lie algebra e6,
which we realize as the the sum of f4, the derivations of the exceptional
Jordan algebra J3 of dimension 3 with octonionic entries, and the right
multiplication by the elements of J3 with vanishing trace. Our parametrization
is a generalization of the Euler angles for SU(2) and it is based on the
fibration of E6 via a F4 subgroup as the fiber. It makes use of a similar
construction we have performed in a previous article for F4. 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 E6 group
manifold.
