The Projective Unitary Irreducible Representations of the Galilei Group in 1+2 Dimensions

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of $G^{\uparrow}_{+}$.