Examples of nonabelian Lie Groups that are easy to visualize Are there some good examples of non-abelian Lie groups $G$ that are easy to visualize?
The "prototypical" abelian one I've been using so far is $G = S^1$, which works great; its Lie Algebra $\mathfrak g = T_e G$ can easily by visualized as the line tangent to $e$ at $S^1$, and so I can easily draw pictures of the exponential map, the left-invariant vector fields, etc. 
I was wondering whether there was a similar good non-abelian example that I could keep in mind.
This question is possibly a duplicate; I admit I don't really understand the answer.

$SO(3,\Bbb R)$ is something we visualize all the time. The associated algebra (which is the set of skew symmetric matrices) has a classical picture as "infinitesimal rotations."
