The Exceptional Simple Lie Algebras F
            <sub>4</sub>
            and E
            <sub>6</sub>

Chevalley, Claude; Schafer, R. D.

doi:10.1073/pnas.36.2.137

Cited by 87 publications

(65 citation statements)

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“…Extending in a similar manner, we find that C⊕V has the structure of an Albert algebra (a type of Jordan algebra) and F 4 is the automorphism group of that algebra; see [32], [148, §7.2], or [107, 26.18].…”

Section: E 8 As An Automorphism Groupmentioning

confidence: 99%

$E_8$, the most exceptional group

Garibaldi

2016

Bull. Amer. Math. Soc.

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Section: E 8 As An Automorphism Groupmentioning

confidence: 99%

$E_8$, the most exceptional group

Garibaldi

2016

Bull. Amer. Math. Soc.

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“…QQ [7,1] = e [7]; QQ [7,2] = e [6]; QQ [7,3] = −e [8]; QQ [7,4] = e [5]; QQ [7,5] = −e [4]; QQ [7,6] = −e [2]; QQ [7,7] = −e [1]; QQ [7,8] %%%% construction of the matrices MT = { {{mt [1], 0, 0, 0, 0, 0, 0, 0}, {mt [2], mt [3], mt [4], mt [5], mt [6], mt [7], mt [8], mt [9]}, {mt [10], mt [11] C The matrices.…”

Section: The Volume Of Ementioning

confidence: 99%

“…Our starting point for the construction of the exceptional algebra e 6 is a Theorem due to Chevalley and Schafer [5] which we rewrite here for convenience We will refer to [8] for the notations. Then the exceptional Jordan algebra is the algebra J 3 .…”

Section: Introductionmentioning

confidence: 99%

Mapping the geometry of the E6 group

Bernardoni

Cacciatori

Cerchiai

et al. 2008

Journal of Mathematical Physics

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In this paper we present a construction for the compact form of the exceptional Lie group E6 by exponentiating 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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“…e $}-the algebra of norm skew transformations in $-is the split Lie algebra £^( [7]). ®(3f) = {derivations of ^} -{D e 8(3) | ID -0} = {£> e £(£) | -JD* -D], # denoting transpose with respect to the trace form, is the split Lie algebra F* ( [7]). QQIΣke,) ^{De 3)(3) or 8(3) 1^ = 0^ = 1, 2, 3} is the split Lie algebra D 4 ([7]).…”

confidence: 99%