# Lie group, derived

From Encyclopedia of Mathematics

The commutator subgroup of a Lie group. For any Lie group its derived Lie group is a normal (not necessarily closed) Lie subgroup of . The corresponding ideal of the Lie algebra of the group coincides with the commutator algebra (also called the derived Lie algebra of ). The commutator subgroup of a simply-connected (or connected linear) Lie group is always closed in .

#### References

[1] | C. Chevalley, "Theory of Lie groups" , 1 , Princeton Univ. Press (1946) |

**How to Cite This Entry:**

Lie group, derived.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Lie_group,_derived&oldid=17709

This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article