With this multiplication, G becomes a group isomorphic to SL ( 2 , C ) , the universal covering group of SO(3; 1). Since each π g has two elements, by the above construction, there is a 2:1 covering map p : G → SO(3; 1). According to covering group theory, the Lie algebras s o ( 3 ; 1 ) , s l ( 2 , C ) and g of G are all isomorphic. The covering map p : G → SO(3; 1) is simply given by p (g, [ p g ]) = g.