In this paper we present a construction for the compact form of the exceptional Lie group E{sub 6} by exponentiating the corresponding Lie algebra e{sub 6}, which we realize as the sum of f{sub 4}, the derivations of the exceptional Jordan algebra J{sub 3} of dimension 3 with octonionic entries, and the right multiplication by the elements of J{sub 3} with vanishing trace. Our parameterization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E{sub 6} via a F{sub 4} subgroup as the fiber. It makes use of a similar construction we ...
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Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (United States)
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In this paper we present a construction for the compact form of the exceptional Lie group E{sub 6} by exponentiating the corresponding Lie algebra e{sub 6}, which we realize as the sum of f{sub 4}, the derivations of the exceptional Jordan algebra J{sub 3} of dimension 3 with octonionic entries, and the right multiplication by the elements of J{sub 3} with vanishing trace. Our parameterization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E{sub 6} via a F{sub 4} subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for F{sub 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{sub 6} group manifold.
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Cerchiai , Bianca; Bernardoni, Fabio; Cacciatori, Sergio L.; Cerchiai, Bianca L. & Scotti, Antonio.Mapping the geometry of the E6 group,
article,
October 1, 2007;
Berkeley, California.
(digital.library.unt.edu/ark:/67531/metadc895124/:
accessed November 19, 2018),
University of North Texas Libraries, Digital Library, digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.
