Semi-Projective Representations and Twisted Schur Multipliers

We study semi-projective representations, i.e., homomorphisms of finite groups to the group of semi-projective transformations of finite dimensional $K$-vector spaces. We extend Schur's concept of projective representation groups to the semi-projective case under the assumption that $K$ is algebraically closed. In order to stress the relevance of the theory, we discuss two important applications, where semi-projective representations occur naturally. The first one reviews Isaacs' treatment of the extension problem of invariant characters (over arbitrary fields) defined on normal subgroups. The second one is our original algebro-geometric motivation and deals with the problem to find linear parts of homeomorphisms and biholomorphisms of complex torus quotients.