====== SO(2) ======

<tabbox 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 $U(1)$.
  
<tabbox 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 [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#so2_2d_4d_reps|Fun with Symmetry]].

[{{ :advanced_tools:group_theory:representation_theory:so2_2d_4d_reps.jpg?nolink }}]
 
<tabbox Abstract> 

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

<tabbox Why is it interesting?>   

/*<tabbox FAQ>*/ 

/*<tabbox History>*/ 

</tabbox>