A more general method to classify up to equivariant KK-equivalence

TL;DR

This paper introduces a generalized classification method for objects in triangulated categories using a homological invariant and an obstruction class, enabling strong classification results for specific C*-algebra actions.

Contribution

It develops a new, more general classification approach combining invariants and obstruction classes for triangulated categories with projective resolutions of length two.

Findings

Classifies circle group actions on C*-algebras

Classifies C*-algebras over finite unique path spaces

Classifies graph C*-algebras with finitely many ideals

Abstract

Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results for actions of the circle group on C*-algebras, C*-algebras over finite unique path spaces, and graph C*-algebras with finitely many ideals.