2021/01/28 by Fan, Qingzhai, Fang, Xiaochun
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2101.11921
In this paper, we introduce a class of generalized tracial approximation \rm C^*-algebras. Let P be a class of unital \rm C^*-algebras which have tracially Z-absorbing (tracial nuclear dimension at most n, \rm SP property, m-almost divisible, weakly (m, n)-divisible). Then A has tracially Z-absorbing (tracial nuclear dimension at most n, \rm SP property, weakly m-almost divisible, secondly weakly (m, n)-divisible) for any simple unital \rm C^*-algebra A in the class of this 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.