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I am reading Naive Lie Theory by John Stillwell, and he gives the definition of a simple Lie group as a Lie group which has no non-trivial normal subgroups.

Wikipedia, on the other hand, defines it as a Lie group which has noconnectednormal subgroups.

I was wondering, which definition is more common in the literature, and which definition did Lie use, etc? There seems to be quite a bit of difference between the two definitions since under the first definition, for example, SU(2) is not simple, [STRIKE]while under the second definition, it is (since it's non-trivial normal subgroups 1 and -1 aren't connected).[/STRIKE]

The first definition is certainly more restrictive, and would eliminate all SU(n) and Sp(n).

EDIT: Wait a second...SU(2) is a connected group so.......even under the second definition, it's not simple right? ... So why do I see it labeled as simple all the time? I'm confused.

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# Simple Lie Group Definition

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