One should note that the terminology differs between mathematics and physics. In the linked article, term "projective representation" has a slightly different meaning, but the term as presented here enters as an ingredient and the mathematics per se is of course the same. If the realization of the symmetry group, , is given in terms of action on the space of unit rays , then it is a projective representation in the mathematical sense, while its representative on Hilbert space is a projective representation in the physical sense.