SCHUR INDEX FOR PROJECTIVE REPRESENTATIONS OF FINITE GROUPS

In this paper the question of determining the absolutely irreducible constituents of an irreducible projective representation the theory of algebras. New proofs are given for several of the main results of the theory of representations of finite dimensional associative algebras. This theory is applied to determine the center of a simple component of a twisted group algebra modulo its radical and sufficient conditions are given to insure that this center is a normal extention of the base field. The Schur index of an absolutely irreducible projective representation of a finite group is defined as in the theory of linear representations of finite groups. It is shown that every irreducible complex projective representation of a finite group is projectively equivalent to a representation whose associated factor system has values which are roots of unity but whose Schur index over the rationale is 1. © 1969 by Pacific Journal of Mathematics.