Clifford Theory with Schur Indices in Projective Representation Theory#

Abstract

For finite groups G, it is shown that central simple G-algebras arise naturally from irreducible modules of twisted group algebras over fields of characteristic 0. This leads to an extension of Turull's Clifford theory with Schur indices that applies in the setting of projective representations of finite groups. This theory has the same properties as in the ordinary representation theory setting, perhaps the most interesting of which is a Schur index preserving bijection between certain sets of irreducible projective characters.