2022/03/11 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.2203.05700
openalex publication_date 2022/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce some classes of generalized tracial approximation \rm C^*-algebras. Consider the class of unital \rm C^*-algebras which are tracially Z-absorbing (or have tracial nuclear dimension at most n, or have the property \rm SP, or are m-almost divisible). Then A is tracially Z-absorbing (respectively, has tracial nuclear dimension at most n, has the property \rm SP, is weakly (n, m)-almost divisible) for any simple unital \rm C^*-algebra A in the corresponding class of generalized tracial approximation \rm C^*-algebras. As an application, let A be an infinite-dimensional unital simple \rm C^*-algebra, and let B be a centrally large subalgebra of A. If B is tracially Z-absorbing, then A is tracially Z-absorbing. This result was obtained by Archey, Buck, and Phillips in \citeAJN.