Symmetric Spaces of Exceptional Groups

2008/11/04 by Boya, Luis J.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0811.0554

Abstract

We adress the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1+2 cases for G₂ and F₄ respectively are easily explained from the octonionic nature of these groups. The 4+3+2 cases on the E_6,7,8 series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in 5, 4 and 3 spacetime dimensions.

Related

• Exceptional groups, symmetric spaces and applications
• Exceptional Lie groups
• The exceptional symmetry
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• Special Riemannian geometries modeled on distinguished symmetric spaces