which are exactly on the form of the 3 -dimensional version of the commutation relations for s o ( 3 ; 1 ) (see conventions and Lie algebra bases below). Thus, the map J i ↔ j i, K i ↔ k i, extended by linearity is an isomorphism. Since SL ( 2 , C ) is simply connected, it is the universal covering group of SO(3; 1).