Cromlech, menhirs and celestial sphere: an unusual representation of the   Lorentz group
  We present a novel representation of the Lorentz group, the geometric version of which uses "reversions" of a sphere while the algebraic version uses pseudounitary 2x2 matrices over complex numbers and quaternions, and Clifford algebras in general. A remarkably simple formula for relativistic composition of velocities and an accompanying geometric construction follows. The method is derived from the diffeomorphisms of the celestial sphere induced by Lorentz boost. 
Jerzy Kocik
math-ph math.MP