# SO(2)

## Intuitive

The Lie group $SO(2)$ describes all possible 2D rotations. The group is one dimensional, that is, it has only one parameter: the rotation angle.

The group $SO(2)$ is isomorphic to $U(1)$.

## Concrete

Representations

The diagram below shows the (2-dimensional) defining representation of $SO(2)$ in its upper branch and a 4-dimensional, reducible representation of the same group in the lower branch. For a more detailed explanation of this diagram and representations of other Lie groups see Fun with Symmetry.

## Abstract

The motto in this section is: the higher the level of abstraction, the better.