nLab
classical Lie group

Contents

Context

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

Idea

The classification of simple Lie groups contains four infinite series of “classical” simple Lie groups:

Apart from this there are five exceptional Lie groups.

graphics grabbed from Schwichtenberg

More generally, other matrix Lie groups, such as the general linear group GL(n)GL(n), may be called “classical”.

References

Last revised on April 8, 2021 at 01:39:36. See the history of this page for a list of all contributions to it.