4.2 Lie Algebra

The Lie algebra $\mathrm{\mathfrak{se}}(2)$ has three generators:

$$G_{1}={\scriptstyle \left(\begin{array}{cc\vert c} 0 & 0 & 1\\ 0 ... ...array}{cc\vert c} 0 & -1 & 0\\ 1 & 0 & 0\\ \hline 0 & 0 & 0 \end{array}\right)}$$ (49)