E8, the most exceptional group

Abstract

The five exceptional simple Lie algebras over the complex number are included one within the other as G2 ⊂ F4 ⊂ E6 ⊂ E7 ⊂ E8. The biggest one, E8, is in many ways the most mysterious. This article surveys what is known about it including many recent results, focusing on the point of view of Lie algebras and algebraic groups over fields.

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