Powers averaging for actions on $C(X)$-algebras

Abstract

Given a unital $C(X)$-algebra $A$ discrete group $\Gamma$ and an action $\alpha :\Gamma \to \text{aut}(A)$ which leaves $C(X)$ invariant and such that $C(X){⋊}_{\alpha ,r}\Gamma$ is simple, and a $2$-cocycle $\omega$, we obtain a bijective correspondence between maximal $\Gamma$-invariant ideals of $A$ and maximal ideals in $A{⋊}_{\alpha ,\omega ,r}\Gamma$. In particular, $A{⋊}_{\alpha ,\omega ,r}\Gamma$ is simple if and only if $A$ has no $\Gamma$-invariant ideals.

Minor Revisions