simple Lie group

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

This is *not* the same thing as a simple object in LieGrp (or even in $Conn Lie Grp$). 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).

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)