where J a , P a , K a , H are generators of rotations (angular momentum operator), spatial translations (momentum operator), Galilean boosts and time translation (Hamiltonian) respectively. (Notes: i is the imaginary unit, i 2 = − − 1 . The specific form of the commutators of the generators of rotation J a is the one of three-dimensional space, then a , b , c = 1 , … … , 3 .). The central extension M has an interpretation as non-relativistic mass and corresponds to the symmetry of Schrödinger equation under phase transformation (and to the conservation of probability).