Mapping the geometry of the F4 group

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In this paper, we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 Hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of ... continued below

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Bernardoni, Fabio; Cacciatori, Sergio L; Scotti, Antonio & Cerchiai, Bianca L. May 28, 2007.

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In this paper, we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 Hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2 = F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup.

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  • Journal Name: Advances in Theoretical and Mathematical Physics; Journal Volume: 12; Journal Issue: 4; Related Information: Journal Publication Date: 2008

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  • Report No.: LBNL-1517E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 948502
  • Archival Resource Key: ark:/67531/metadc895265

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  • May 28, 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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Bernardoni, Fabio; Cacciatori, Sergio L; Scotti, Antonio & Cerchiai, Bianca L. Mapping the geometry of the F4 group, article, May 28, 2007; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc895265/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.