Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups.
We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain why any connected Lie groups is the quotient of a simply connected Lie group (its universal covering space) by a discrete subgroup, and work out some examples of universal covering groups.
For the other lectures in the course see • Lie groups