The Rokhlin property and the tracial topological rank
| dc.creator | Lin, Huaxin | |
| dc.creator | Osaka, Hiroyuki | |
| dc.date | 2004-02-06 | |
| dc.date | 2004-03-09 | |
| dc.date.accessioned | 2026-07-07T05:05:11Z | |
| dc.date.available | 2026-07-07T05:05:11Z | |
| dc.description | Let $A$ be a unital separable simple \CA with $\tr(A)\le 1$ and $α$ be an automorphism. We show that if $α$ satisfies the tracially cyclic Rokhlin property then $\tr(A\rtimes_α\Z)\le 1.$ We also show that whenever $A$ has a unique tracial state and $α^m$ is uniformly outer for each $m (\not= 0)$ and $α^r$ is approximately inner for some $r>0,$ $α$ satisfies the tracial cyclic Rokhlin property. By applying the classification theory of nuclear \CA s, we use the above result to prove a conjecture of Kishimoto: if $A$ is a unital simple $A{\mathbb T}$-algebra of real rank zero and $α\in \Aut(A)$ which is approximately inner and if $α$ satisfies some Rokhlin property, then the crossed product $A\rtimes_α\Z$ is again an $A{\mathbb T}$ -algebra of real rank zero. As a by-product, we find that one can construct a large class of simple \CA s with tracial rank one (and zero) from crossed products. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402094 | |
| dc.identifier | http://arxiv.org/abs/math/0402094 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70080 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05; 46L35 | |
| dc.title | The Rokhlin property and the tracial topological rank | |
| dc.type | text |