𝐸₈, the most exceptional group

Garibaldi, Skip

doi:10.1090/bull/1540

$E_8$, the most exceptional group
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Bull. Amer. Math. Soc. 53 (2016), 643-671 Request permission

Abstract:

The five exceptional simple Lie algebras over the complex number are included one within the other as $\mathfrak {g}_2 \subset \mathfrak {f}_4 \subset \mathfrak {e}_6 \subset \mathfrak {e}_7 \subset \mathfrak {e}_8$. The biggest one, $\mathfrak {e}_8$, is in many ways the most mysterious. This article surveys what is known about it, including many recent results, and it focuses on the point of view of Lie algebras and algebraic groups over fields.

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