Projective Representation

In the mathematical field of representation theory, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group

PGL(V,F) = GL(V,F)/F

where GL(V,F) is the general linear group of invertible linear transformations of V over F and F* here is the normal subgroup consisting of multiplications of vectors in V by nonzero elements of F (that is, scalar multiples of the identity; scalar transformations).

Read more about Projective Representation:  Linear Representations and Projective Representations, Projective Representations of Lie Groups