Editing One-parameter group (section)

==Examples==
In [[Lie theory]], one-parameter groups correspond to one-dimensional subspaces of the associated [[Lie algebra]]. The [[Lie group–Lie algebra correspondence]] is the basis of a science begun by [[Sophus Lie]] in the 1890s.

Another important case is seen in [[functional analysis]], with <math>G</math> being the group of [[unitary operator]]s on a [[Hilbert space]]. See [[Stone's theorem on one-parameter unitary groups]].

In his monograph ''Lie Groups'', [[P. M. Cohn]] gave the following theorem:
:Any connected 1-dimensional Lie group is analytically isomorphic either to  the additive group of real numbers <math>\mathfrak{R}</math>, or to <math>\mathfrak{T}</math>, the additive group of real numbers <math>\mod 1</math>. In particular, every 1-dimensional Lie group is locally isomorphic to <math>\mathbb{R}</math>.<ref>[[Paul Cohn]] (1957) ''Lie Groups'', page 58, Cambridge Tracts in Mathematics and Mathematical Physics #46</ref>