Let 0 →I → A →A/I →0 be a short exact sequence of C^＊-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I belongs to a class of certain C^＊-algebras. We show that A has t...Let 0 →I → A →A/I →0 be a short exact sequence of C^＊-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I belongs to a class of certain C^＊-algebras. We show that A has trazial topological rank no more than one if the extension is quasidiagonal, and A has the property （P1） if the extension is tracially quasidiagonal.展开更多
A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more...A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11071188)
文摘Let 0 →I → A →A/I →0 be a short exact sequence of C^＊-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I belongs to a class of certain C^＊-algebras. We show that A has trazial topological rank no more than one if the extension is quasidiagonal, and A has the property （P1） if the extension is tracially quasidiagonal.
文摘A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.
