A more systematic notation allows to cast these generators into the four (infinite) families X n , Y m ( j ) , M n and R n ( j k ) = − − R n ( k j ) , where n ∈ ℤ is an integer and m ∈ ℤ+1/2 is a half-integer and j,k=1,...,d label the spatial direction, in d spatial dimensions. The non-vanishing commutators of the Schrödinger algebra become (euclidean form)