But exp : s o ( 3 ; 1 ) → → SO ( 3 ; 1 ) + is surjective. One way to show this is to make use of the isomorphism SO ( 3 ; 1 ) + ≅ ≅ PGL ( 2 , C ) , the latter being the Möbius group. It is a quotient of GL ( n , C ) (see the linked article). The quotient map is denoted with p : GL ( n , C ) → → PGL ( 2 , C ) . The map exp : g l ( n , C ) → → GL ( n , C ) is onto. Apply (Lie) with π being the differential of p at the identity. Then