$E_8$, the most exceptional group

Abstract

The five exceptional simple Lie algebras over the complex number are included one within the other as $G_2\subset F_4\subset E_6\subset E_7\subset E_8$. The biggest one, $E_8$, 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.

References in corpus (4)

• The sphere packing problem in dimension 8
• Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild
• Sporadic and Exceptional
• The Kneser-Tits conjecture for groups with Tits-index E_{8,2}^{66} over an arbitrary field

Cited by in corpus (7)

• A non-Abelian twist to integer quantum Hall states
• Exceptional Unification of Families and Forces
• A class of continuous non-associative algebras arising from algebraic groups including $E_8$
• Time, E8, and the Standard Model
• Sculpting the Standard Model from low-scale Gauge-Higgs-Matter $E_8$ Grand Unification in ten dimensions
• Modular curves, invariant theory and $E_8$
• Linear models of the exceptional Lie algebra ${\mathfrak{e}}_8$