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.
Why is it interesting?
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