nLab exceptional Lie group



Exceptional structures

Group Theory

Lie theory

∞-Lie theory (higher geometry)


Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids



Related topics


\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras



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

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


Lie groups

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

Cohomological properties are discussed in

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

Last revised on November 25, 2023 at 20:08:02. See the history of this page for a list of all contributions to it.