Bijections Between Sets of Invariant Ideals, Via the Ladder Technique

TL;DR

This paper introduces a new ladder technique to establish a lattice isomorphism between invariant ideals of C*-algebras and their crossed products, extending known results beyond amenable groups to all locally compact groups.

Contribution

It presents a novel method for bijections between invariant ideals in C*-algebras and crossed products, applicable to all locally compact groups.

Findings

Establishes a lattice isomorphism for non-amenable groups

Extends known correspondence to broader class of groups

Introduces the ladder technique for ideal analysis

Abstract

We present a new method of establishing a bijective correspondence - in fact, a lattice isomorphism - between action- and coaction-invariant ideals of C*-algebras and their crossed products by a fixed locally compact group. It is known that such a correspondence exists whenever the group is amenable; our results hold for any locally compact group under a natural form of coaction invariance.