It is these properties of K and J under P that motivate the terms vector for K and pseudovector or axial vector for J. In a similar way, if π is any representation of s o ( 3 ; 1 ) and Π is its associated group representation, then Π(SO(3; 1)) acts on the representation of π by the adjoint action, π (X) ↦ Π(g) π (X) Π(g) for X ∈ ∈ s o ( 3 ; 1 ) , g ∈ SO(3; 1). If P is to be included in Π, then consistency with (F1) requires that