Ideal Structure of Semigroup Crossed Products by Endomorphisms

Abstract

Given a cyclically ordered free abelian group $G$, a C$^*$-algebra $A$ which is not necessarily unital and an action $\alpha$ of the positive cone $P(G)$ by endomorphisms of $A$. We consider ideals of $A$ and how do they relate with the ideals of the semigroup crossed product $A\times_\alpha P(G)$