Mapping the geometry of the E6 group
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.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- Physics Division
- DOE Contract Number:
- DE-AC02-05CH11231
- OSTI ID:
- 934760
- Report Number(s):
- LBNL-443E; TRN: US0803858
- Journal Information:
- Journal of Mathematical Physics, Vol. 49; Related Information: Journal Publication Date: 30 January 2008
- Country of Publication:
- United States
- Language:
- English
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