Decomposition of idempotent 2-cocycles

Abstract

Let L be a finite Galois field extension of K with Galois group G. We decompose any idempotent 2-cocycle f using finite sequences of descending two-sided ideals of the corresponding weak crossed product algebra Af . We specialize the results in case f is the corresponding idempotent 2-cocycle fr for some semilinear map r ∶ G → Ω, where Ω is a multiplicative monoid with minimum element.