Mapping the geometry of the E6 group Page: 1 of 31
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Mapping the geometry of the E6 group
Fabio Bernardonil*, Sergio L. Cacciatori2t, Bianca L. Cerchiai1 and
1Departament de Fisica Teorica, IFIC, Universitat de Valencia - CSIC
Apt. Correus 22085, E-46071 Valencia, Spain.
2 Dipartimento di Scienze Fisiche e Matematiche,
Via Valleggio 11, I-22100 Como.
3 Lawrence Berkeley National Laboratory
Theory Group, Bldg 50A5104
1 Cyclotron Rd, Berkeley CA 94720 USA
4 Dipartimento di Matematica dell'Universit di Milano,
Via Saldini 50, I-20133 Milano, Italy.
5 INFN, Sezione di Milano, Via Celoria 16, 1-20133 Milano.
In this paper we present a construction for the compact form of the exceptional Lie group E6 by expo-
nentiating 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
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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. (https://digital.library.unt.edu/ark:/67531/metadc895124/m1/1/: accessed March 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.