If π and Π are the standard representations on R 4 and if the action is restricted to s o ( 3 , 1 ) ⊂ ⊂ End ( R 4 ) , then the two above representations are the adjoint representation of the Lie algebra and the adjoint representation of the group respectively. The corresponding representations (some R n or C n ) always exist for any matrix Lie group, and are paramount for investigation of the representation theory in general, and for any given Lie group in particular.