nLab exceptional Lie group

Idea

The exceptional Lie groups are the exceptional structures among the simple Lie groups.

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 Lie algebra

• exceptional geometry, exceptional generalized geometry

• universal exceptionalism

• Freudenthal magic square

References

Lie groups

• Ichiro Yokota, Exceptional Lie groups [arXiv:0902.0431]

Lie algebras

Original articles include

• Hans Freudenthal, Lie groups in the foundations of geometry, Advances in Mathematics, volume 1, (1965) pp. 145 - 190 (dspace)

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)

• John Baez, Exceptional Lie algebras, chapter 4 in The Octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205. (web)

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)