Is a Lie group connected?

Question

I want to know if a Lie group is connected in general situation.I also want some example of Lie group. I will appreciate your help.

Answer 1

Lie groups need not be connected in general. Examples are the isometry groups of compact Riemannian manifolds. They are nonconnected Lie groups. Many examples of Lie groups arise from classical matrix groups. For more references see here.