Editing Lie group (section)

=== Dimensions one and two ===
The only connected Lie groups with dimension one are the real line <math>\mathbb{R}</math> (with the group operation being addition) and the [[circle group]] <math>S^1</math> of complex numbers with absolute value one (with the group operation being multiplication). The <math>S^1</math> group is often denoted as {{tmath|1= \operatorname{U}(1) }}, the group of <math>1\times 1</math> unitary matrices.

In two dimensions, if we restrict attention to simply connected groups, then they are classified by their Lie algebras. There are (up to isomorphism) only two Lie algebras of dimension two. The associated simply connected Lie groups are <math>\mathbb{R}^2</math> (with the group operation being vector addition) and the affine group in dimension one, described in the previous subsection under "first examples".