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+====== Sp(1) ======
+<tabbox Intuitive>
+$Sp(1)$ is the group of quaternions of unit length, also known as the compact symplectic group of order one, hence the name $Sp(1)$. (See [[https://math.ucr.edu/home/baez/symplectic.html]] for an explanation of the name.)
+The group $Sp(1)$ is isomorphic to $SU(2)$.
+<tabbox Concrete>
+**Representations**
+The diagram below shows the defining representation of $Sp(1)$ in its upper branch and the (3-dimensional) adjoint  representation of the same group in the lower branch. The latter representation can be used to rotate objects in 3D space and has applications in computer graphics. For a more detailed explanation of this diagram and representations of other Lie groups see [[https://esackinger.wordpress.com/|Fun with Symmetry]].
+[{{ :advanced_tools:group_theory:representation_theory:sp1_quaternions.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>