2023/10/19 by George A. Elliott, Elliott, George A., Qingzhai Fan +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2310.12548
openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Ω be a class of \rm C^*-algebras. In this paper, we study a class of not necessarily unital generalized tracial approximation \rm C^*-algebras, and the class of simple \rm C^*-algebras which can be generally tracially approximated by \rm C^*-algebras in Ω, denoted by \rm gTAΩ. Let Ω be a class of unital \rm C^*-algebras and let A be a simple unital \rm C^*-algebra. Then A∈ \rm gTAΩ, if, and only if, A∈ \rm WTAΩ (where \rm TAΩ is the class of weakly tracially approximable unital \rm C^*-algebras introduced by Elliott, Fan, and Fang).Consider the class of \rm C^*-algebras which are tracially Z-absorbing (or are of tracial nuclear dimension at most n, or are m-almost divisible, or have the property \rm SP). Then A is tracially Z-absorbing (respectively, has tracial nuclear dimension at most n, is weakly (n, m)-almost divisible, has the property \rm SP) for any simple \rm C^*-algebra A in the corresponding class of generalized tracial approximation \rm C^*-algebras.