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

2000/11/13 by Huaxin Lin, Lin, Huaxin
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/0011079

arxiv created 2000/11/13 · openalex publication_date 2000/11/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a classification theorem for unital separable simple nuclear C^*-algebras with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if A and B are two such C^*-algebras and (K₀(A), K₀(A)₊, [1_A], K₁(A)) ≅ (K₀(B), K₀(B)₊, [1_B], K₁(B)), then A≅ B.

Related

• Simple nuclear C^*-algebras of tracial topological rank one
• On classification of non-unital simple amenable C*-algebras, I
• Classifying ^*-homomorphisms I: Unital simple nuclear C^*-algebras
• On classification of simple non-unital amenable C*-algebras, II
• Applications of C^*-classification