scholarly journals The Rokhlin property and the tracial topological rank

2005 ◽  
Vol 218 (2) ◽  
pp. 475-494 ◽  
Author(s):  
Huaxin Lin ◽  
Hiroyuki Osaka
Keyword(s):  
Tracial Topological Rank

The tracial topological rank of certain C*-algebras

2011 ◽  
Vol 54 (11) ◽  
pp. 2295-2307 ◽  
Author(s):  
XiaoChun Fang ◽  
YiLe Zhao
Keyword(s):  
C Algebras ◽  
Tracial Topological Rank

scholarly journals The tracial topological rank of extensions of $C^*$-algebras

2004 ◽  
Vol 94 (1) ◽  
pp. 125 ◽  
Author(s):  
Shanwen Hu ◽  
Huaxin Lin ◽  
Yifeng Xue
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Rank Zero ◽  
C Algebras ◽  
Tracial Topological Rank ◽  
Quasidiagonal Extension

Let $0\to \mathcal J\to \mathcal A\to \mathcal A / \mathcal J\to 0$ be a short exact sequence of separable $C^*$-algebras. We introduce the notion of tracially quasidiagonal extension. Suppose that $\mathcal J$ and $\mathcal A/J$ have tracial topological rank zero. We prove that if $(\mathcal A, \mathcal J)$ is tracially quasidiagonal, then $\mathcal A$ has tracial topological rank zero.

Tracially Quasidiagonal Extensions

2003 ◽  
Vol 46 (3) ◽  
pp. 388-399 ◽  
Author(s):  
Huaxin Lin
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Tracial Topological Rank ◽  
Unital Simple ◽  
Quasidiagonal Extension

AbstractIt is known that a unital simple C*-algebra A with tracial topological rank zero has real rank zero. We show in this note that, in general, there are unital C*-algebras with tracial topological rank zero that have real rank other than zero.Let 0 → J → E → A → 0 be a short exact sequence of C*-algebras. Suppose that J and A have tracial topological rank zero. It is known that E has tracial topological rank zero as a C*-algebra if and only if E is tracially quasidiagonal as an extension. We present an example of a tracially quasidiagonal extension which is not quasidiagonal.

The Tracial Topological Rank of $C^*$-algebras (II)

2004 ◽  
Vol 53 (6) ◽  
pp. 1579-1606 ◽  
Author(s):  
Shanwen Hu ◽  
Huaxin Lin ◽  
Yifeng Xue
Keyword(s):  
C Algebras ◽  
Tracial Topological Rank

scholarly journals TRACIAL EQUIVALENCE FOR $C^*$-ALGEBRAS AND ORBIT EQUIVALENCE FOR MINIMAL DYNAMICAL SYSTEMS

2005 ◽  
Vol 48 (3) ◽  
pp. 673-690
Author(s):  
Huaxin Lin
Keyword(s):  
Dynamical Systems ◽  
Crossed Products ◽  
Rank Zero ◽  
C Algebras ◽  
Orbit Equivalent ◽  
Linear Maps ◽  
Positive Linear Maps ◽  
Tracial Topological Rank ◽  
Minimal Dynamical Systems ◽  
Cantor Minimal Systems

AbstractWe introduce the notion of tracial equivalence for $C^*$-algebras. Let $A$ and $B$ be two unital separable $C^*$-algebras. If they are tracially equivalent, then there are two sequences of asymptotically multiplicative contractive completely positive linear maps $\phi_n:A\to B$ and $\psi_n:B\to A$ with a tracial condition such that $\{\phi_n\circ\psi_n\}$ and $\{\psi_n\circ\phi_n\}$ are tracially approximately inner. Let $A$ and $B$ be two unital separable simple $C^*$-algebras with tracial topological rank zero. It is proved that $A$ and $B$ are tracially equivalent if and only if $A$ and $B$ have order isomorphic ranges of tracial states. For the Cantor minimal systems $(X_1,\sigma_1)$ and $(X_2,\sigma_2)$, using a result of Giordano, Putnam and Skau, we show that two such dynamical systems are (topological) orbit equivalent if and only if the associated crossed products $C(X_1)\times_{\sigma_1}\mathbb{Z}$ and $C(X_2)\times_{\sigma_2}\mathbb{Z}$ are tracially equivalent.

K-THEORY OF C*-ALGEBRAS WITH TRACIAL TOPOLOGICAL RANK k

2003 ◽  
Vol 14 (02) ◽  
pp. 153-170 ◽  
Author(s):  
SHANWEN HU ◽  
HUAXIN LIN ◽  
YIFENG XUE
Keyword(s):  
C Algebras ◽  
K Theory ◽  
Tracial Topological Rank

We show that if [Formula: see text] has tracial topological rank no more than k, then [Formula: see text] and if p, q ∈ A are two projections with [p] = [q] in [Formula: see text], then [Formula: see text] Other results for K0(A) are also established.

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