On Invariants of $\text{C}^*$-algebras with the ideal property

TL;DR

This paper demonstrates that for C*-algebras with the ideal property, two related invariants are isomorphic, unifying previous invariants like Elliott's and Stevens' invariants within this class.

Contribution

The paper establishes an isomorphism between two categories of invariants for C*-algebras with the ideal property, unifying Elliott's and Stevens' invariants.

Findings

Two categories of invariants are isomorphic for C*-algebras with the ideal property.

Elliott's and Stevens' invariants are isomorphic in this context.

Unification of invariants simplifies classification of these C*-algebras.

Abstract

In this paper, we consider $\text{C}^*$-algebras with the ideal property (the ideal property unifies the simple and real rank zero cases). We define two categories related the invariants of the $\text{C}^*$-algebras with the ideal property. And we showed that these two categories are in fact isomorphic. As a consequence, the Elliott's Invariant and the Stevens' Invariant are isomorphic for $\text{C}^*$-algebras with the ideal property.