Since π 1 (SO(3; 1)) has two elements, some representations of the Lie algebra will yield projective representations. Once it is known whether a representation is projective, formula (G2) applies to all group elements and all representations, including the projective ones — with the understanding that the representative of a group element will depend on which element in the Lie algebra (the X in (G2)) is used to represent the group element in the standard representation.