# Simple Lie group

ANALOGY: This is an analogue in Lie group of a property encountered in group. Specifically, it is a Lie group property analogous to the group property: simple group

View other analogues of simple group | View other analogues in Lie groups of group properties (OR, View as a tabulated list)

## Definition

### Symbol-free definition

A Lie group is said to be **simple** if it does not contain any proper nontrivial connected normal subgroup. (sometimes the definition also requires the Lie group to be connected. Since the connected component is either the whole group or the trivial subgroup, this is not a great loss).

### Definition with symbols

**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE]