Is there a special name for this discrete subgroup of Mobius group with single element:
$$A=\begin{bmatrix}0 & i\\-i & 0\end{bmatrix}$$
and $\det A=-1$ and $A^2=I$.
Thanks- mike
EDIT: $$A=-\sigma_y=-\begin{bmatrix}0 & -i\\i & 0\end{bmatrix}$$
where $\sigma_y$ is one of the Pauli matrices. Pauli matrices are used to describe spin $\frac12$ particle (Fermion) in $R^3$. And $\sigma_y$ alone can be used to describe spin$\frac12$ particle (Fermion) in x-z plane ($R^2$), for example electrons moving in x-z plane under the influence of strong magnetic field $B$ in y direction.
The relevant topics in mathematics are spin group, spinor, and Clifford algebras etc.