The Schrödinger algebra is finite-dimensional and contains the generators X − − 1 , 0 , 1 , Y − − 1 / 2 , 1 / 2 ( j ) , M 0 , R 0 ( j k ) . In particular, the three generators X − − 1 = H , X 0 = D , X 1 = C span the sl(2,R) sub-algebra. Space-translations are generated by Y − − 1 / 2 ( j ) and the Galilei-transformations by Y 1 / 2 ( j ) .