Abstract
The exceptional algebras of typeE 7 are studied from the point of view of their three graded structure. The connection between three-grading and the Jordan Pair structure of such Lie algebras is analyzed. The Jordan Pair content is in turn related to the symmetric spaces
and
. Coset spaces of this type have been recently suggested as possible scalar manifolds in supergravity. We develop a way of representingE 7 in a matrix form, which makes the Jordan Pair content of theE 7 real and complex forms quite transparent and shows whether such forms admit a three graded structure.
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Truini, P., Olivieri, G. & Biedenharn, L.C. Three graded exceptional algebras and symmetric spaces. Z. Phys. C - Particles and Fields 33, 47–65 (1986). https://doi.org/10.1007/BF01410452
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DOI: https://doi.org/10.1007/BF01410452