What does it mean to say a Lie group is real?

[pellman]

What makes a Lie group a real Lie group? I see on the Wikipedia page http://en.wikipedia.org/wiki/Lie_group "A real Lie group is a group that is also a finite-dimensional real smooth manifold" So when is a manifold a real manifold?

 

[branch]

If the charts of your atlas map into R^n the manifold is real, if they map intor C^n it is complex.

 

[pellman]

Thanks. Makes sense.