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

Abstract

In this paper, we consider ${\text{C}}^{\ast }$-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 ${\text{C}}^{\ast }$-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 ${\text{C}}^{\ast }$-algebras with the ideal property.

References in corpus (1)

• A classification of inductive limit $C^{\ast }$-algebras with ideal property