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
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