What do we mean by 'Equivalent Projective representation"? I know that we say two representations R and R' of a group G is equivalent if there exists a unitary matrix U such that URU^(-1)=R'. But what do we mean by equivalent projective rerpesentations? I've heard of the theorem that the SO(3) group has only 2 inequivalent projective representations. But what does that exactly mean? I am very interested in projective representation because it's projective representation rather than ordinary representation that represents symmetry in Quantum Mechanics since the vector A and exp(id)A represent the same physical state. So does anyone know if there are some books that can serve as an introduction to projective representations?