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Total Cuntz semigroup, extension, and Elliott Conjecture with real rank zero.
- Source :
-
Proceedings of the London Mathematical Society . Apr2024, Vol. 128 Issue 4, p1-40. 40p. - Publication Year :
- 2024
-
Abstract
- In this paper, we exhibit two unital, separable, nuclear C∗${\rm C}^*$‐algebras of stable rank one and real rank zero with the same ordered scaled total K‐theory, but they are not isomorphic with each other, which forms a counterexample to the Elliott Classification Conjecture for real rank zero setting. Thus, we introduce an additional normal condition and give a classification result in terms of the total K‐theory. For the general setting, with a new invariant, the total Cuntz semigroup [2], we classify a large class of C∗${\rm C}^*$‐algebras obtained from extensions. The total Cuntz semigroup, which distinguishes the algebras of our counterexample, could possibly classify all the C∗${\rm C}^*$‐algebras of stable rank one and real rank zero. [ABSTRACT FROM AUTHOR]
- Subjects :
- *C*-algebras
*LOGICAL prediction
*K-theory
Subjects
Details
- Language :
- English
- ISSN :
- 00246115
- Volume :
- 128
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Proceedings of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 176635414
- Full Text :
- https://doi.org/10.1112/plms.12595