Module correspondences for twisted group algebras

摘要

Let G and A be finite groups such that (G, A) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K(alpha)G the twisted group algebra of G over K with factor set alpha. In this paper we prove that if A acts homogeneously on K(alpha)G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K(alpha)G-modules and the set of irreducible (KCG)-C-alpha(A)-modules. References: 11