Non-amenable simple C*-algebras with tracial approximation
Xuanlong Fu, Huaxin Lin

TL;DR
This paper constructs two types of simple, separable C*-algebras with the same Elliott invariant as the Jiang-Su algebra, one exact and one non-exact, and analyzes their tracial approximation properties and classification.
Contribution
It introduces new examples of simple C*-algebras with prescribed invariants, including non-amenable and non-exact cases, expanding the understanding of tracial approximation and classification.
Findings
Constructed non-amenable simple C*-algebras with Jiang-Su invariant.
Demonstrated these algebras are essentially tracially in Z-stable class.
Provided models covering all weakly unperforated Elliott invariants.
Abstract
We construct two types of unital separable simple -alebras and one is exact but not amenable, and the other is non-exact. Both have the same Elliott invariant as the Jiang-Su algebra, namely, has a unique tracial state, and (). We show that () is essentially tracially in the class of separable -stable -alebras of nuclear dimension 1. has stable rank one, strict comparison for positive elements and no 2-quasitrace other than the unique tracial state. We also produce models of unital separable simple non-exact -alebras which are essentially tracially in the class of simple separable nuclear -stable -alebras and the models exhaust all possible weakly unperforated…
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Noncommutative and Quantum Gravity Theories
