One may consider a central extension of the Lie algebra of the Galilean group, spanned by H ′, P ′ i, C ′ i, L ′ ij and an operator M : The so-called Bargmann algebra is obtained by imposing [ C i ′ , P j ′ ] = i M δ δ i j , such that M lies in the center, i.e. commutes with all other operators.