SO(2) simple but not semisimple?

[copernicus1]

I read in Mirman's book on group theory that SO(2) is the only simple group that is not semisimple. Can anyone explain this in terms a beginner could understand? I'm not sure how this is possible based on what I've read. Simple groups would seem to be a special case of semisimple groups.

 

[Stephen Tashi]

I notice the Wikipedia article on List of Simple Lie Groups (http://en.wikipedia.org/wiki/List_of_simple_Lie_groups) says

Simple Lie groups

Unfortunately, there is no generally accepted definition of a simple Lie group. In particular, it is not necessarily defined as a Lie group that is simple as an abstract group. Authors differ on whether a simple Lie group has to be connected, or on whether it is allowed to have a non-trivial center, or on whether R is a simple Lie group.

The most common definition implies that simple Lie groups must be connected, and non-abelian, but are allowed to have a non-trivial center.

- which is more than I know about the subject.