Classification of simple $C^*$-algebras of tracial topological rank zero
Huaxin Lin

TL;DR
This paper establishes a classification theorem for unital separable simple nuclear $C^*$-algebras with tracial topological rank zero, showing they are isomorphic if their K-theoretic invariants match, under the Universal Coefficient Theorem.
Contribution
It provides a complete classification of a class of $C^*$-algebras using K-theoretic invariants, extending the understanding of their structure.
Findings
Classification based on K-theoretic invariants is complete for these algebras.
Isomorphism is determined by matching $K_0$, $K_1$, and related data.
The result applies to algebras satisfying the Universal Coefficient Theorem.
Abstract
We give a classification theorem for unital separable simple nuclear -algebras with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if and are two such -algebras and then
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Noncommutative and Quantum Gravity Theories
