Lie group, derived

From Encyclopedia of Mathematics
Revision as of 17:22, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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 .


[1] C. Chevalley, "Theory of Lie groups" , 1 , Princeton Univ. Press (1946)
How to Cite This Entry:
Lie group, derived. Encyclopedia of Mathematics. URL:,_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