Lie group, derived
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 .
|||C. Chevalley, "Theory of Lie groups" , 1 , Princeton Univ. Press (1946)|
Lie group, derived. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lie_group,_derived&oldid=17709