Twisted group algebras of Abelian groups

We study twistings for finite Abelian groups over fields and then show how to extend the notion of idempotent determined by a subgroup, so useful in the case of group algebras, to the case of twisted group algebras, at least when the subgroup is cyclic. In doing so, we obtain a method to compute in a direct way the primitive central idempotents of these algebras over a finite field and fully describe their simple components. (c) 2024 Elsevier Inc. All rights reserved.