A Lie group is a group which is a smooth manifold such that the multiplication and inversion are smooth.
When does a Lie group become simple? What is the difference between simple and semi-simple Lie group?
Just want a quick answer here. Thanks
2026-05-06 10:00:05.1778061605
simple Lie groups
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A simple Lie group is a Lie group that contains no $connected$ normal subgroups. This is not the same as being a Lie group which is simple as an abstract group. For example the real numbers under addition are a simple Lie group, but have plenty of discrete normal subgroups (the integers for example), and even dense normal subgroups (like the rational numbers) which are disconnected under the subspace topology.