The group PSL(2,C) is isomorphic to the (proper) Lorentz group, and its action on the two-sphere agrees with the action of the Lorentz group on the celestial sphere in Minkowski space.
The complete set of symmetries of the Riemann sphere are described by the Möbius transformation group PSL(2,C), which is isomorphic as a real Lie group to the Lorentz group.