nLab
simple Lie group

Context

\infty-Lie theory

∞-Lie theory

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

Simple Lie groups

Definition

A simple Lie group is a connected Lie group with exactly two connected normal subgroups that is not abelian.

Remarks

This is not the same thing as a simple object in LieGrp (or even in ConnLieGrpConn Lie Grp). However, the Lie algebra associated to a simple Lie group is always a simple Lie algebra (although that definition also requires a non-abelian clause).

Classification

The classification of simple Lie groups consists of four infinite series – the classical Lie groups – and five separate cases – the exceptional Lie groups.

See Wikipedia's list of simple Lie groups.

See also at ADE classification

Revised on June 13, 2014 05:11:53 by Urs Schreiber (145.116.130.115)