Abelian Lie group
In geometry, an abelian Lie group is a Lie group that is an abelian group.
A connected abelian real Lie group is isomorphic to. In particular, a connected abelian compact Lie group is a torus; i.e., a Lie group isomorphic to. A connected complex Lie group that is a compact group is abelian and a connected compact complex Lie group is a complex torus; i.e., a quotient of by a lattice.
Let A be a compact abelian Lie group with the identity component. If is a cyclic group, then is topologically cyclic; i.e., has an element that generates a dense subgroup.Citations
