SU(1,1)
= SU(1,1)
{c}
{title2=$|\alpha|^2-|\beta|^2=1$}
Matrices $\begin{pmatrix}\alpha&\beta\\\beta^*&\alpha^*\end{pmatrix}$ with the displayed constraint form a real three-dimensional noncompact <Lie group>. A real <Lie algebra> basis is $m_1=\sigma_x/2$, $m_2=\sigma_y/2$, $m_3=i\sigma_z/2$, with $[m_1,m_2]=m_3$, $[m_2,m_3]=-m_1$, and $[m_3,m_1]=-m_2$.