Mapping the geometry of the E6 group

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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 ... continued below

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Cerchiai , Bianca; Bernardoni, Fabio; Cacciatori, Sergio L.; Cerchiai, Bianca L. & Scotti, Antonio October 1, 2007.

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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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  • Journal Name: Journal of Mathematical Physics; Journal Volume: 49; Related Information: Journal Publication Date: 30 January 2008

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  • Report No.: LBNL-443E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 934760
  • Archival Resource Key: ark:/67531/metadc895124

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  • October 1, 2007

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  • Sept. 27, 2016, 1:39 a.m.

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  • Sept. 30, 2016, 6:48 p.m.

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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 August 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.