Mapping the geometry of the E{sub 6} group

Journal Article · Tue Jan 15 04:00:00 EST 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2830522· OSTI ID:21013807

Bernardoni, Fabio ^[1]; Cacciatori, Sergio L ^[2]; Cerchiai, Bianca L ^[3]; Scotti, Antonio ^[4]

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1. Departament de Fisica Teorica, IFIC, Universitat de Valencia-CSIC Apt. Correus 22085, E-46071 Valencia (Spain)
2. Dipartimento di Scienze Fisiche e Matematiche, Universita dell'Insubria, Via Valleggio 11, I-22100 Como (Italy)
3. Theory Group, Lawrence Berkeley National Laboratory, Building 50A5104, 1 Cyclotron Road, Berkeley, California 94720 (United States)
4. Dipartimento di Matematica, Universita di Milano, Via Saldini 50, I-20133 Milan (Italy)

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 parametrization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E{sub 6} via an 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.

• OSTI ID: 21013807
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 1 Vol. 49; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
GEOMETRY
GRAND UNIFIED THEORY
MAPPING
SU-2 GROUPS
SYMMETRY BREAKING