nLab
exceptional Lie group

Idea

The classification of simple Lie groups consists of four infinite series – the classical Lie groups, and five exceptional Lie groups, called

• G2, F4, E6, E7, and E8.

On the level of Kac-Moody Lie algebras/Kac-Moody groups the E-series continues as

• E9, E10, E11, …

Related concepts

• exceptional geometry, exceptional generalized geometry

References

Lie groups

• Ichiro Yokota, Exceptional Lie groups (arXiv:0902.0431)

Lie algebras

The following are references on the Lie algebras underlying exceptional Lie groups.

Surveys include

• wikipedia, En

• J. R. Faulkner, J. C. Ferrar, Exceptional Lie algebras and related algebraic and geometric structures, (pdf)

Geometric constructions of exceptional Lie algebras are discussed in

• José Figueroa-O’Farrill, A geometric construction of the exceptional Lie algebras F4 and E8 (arXiv:0706.2829)

• Andrei Moroianu, Uwe Semmelmann, Invariant four-forms and symmetric pairs (arXiv:1202.3407)

Cohomological properties are discussed in

• Skip Garibaldi, Cohomological invariants: Exceptional groups and spin groups Memoirs of the AMS 937 (2009)