Embedding Crossed Products into a Unital Simple AF-algebra
| dc.creator | Lin, Huaxin | |
| dc.date | 2006-04-03 | |
| dc.date.accessioned | 2026-07-07T07:10:27Z | |
| dc.date.available | 2026-07-07T07:10:27Z | |
| dc.description | Let $X$ be a compact metric space and let $\af$ be a homeomorphism on $X.$ Related to a theorem of Pimsner, we show that $C(X)\rtimes_{\af}\Z$ can be embedded into a unital simple AF-algebra if and only if there is a strictly positive $\af$-invariant Borel probability measure. Suppose that $Λ$ is a $\Z^d$ action on $X.$ If $C(X)\rtimes_Λ\Z$ can be embedded into a unital simple AF-algebra, then there must exist a strictly positive $Λ$-invariant Borel probability measure. We show that, if in addition, there is a generator $\af_1$ of $Λ$ such that $(X, \af_1)$ is minimal and unique ergodic, then $C(X)\rtimes_Λ\Z^d$ can be embedded into a unital simple AF-algebra with a unique tracial state. Let $A$ be a unital separable amenable simple \CA with tracial rank zero and with a unique tracial state which satisfies the Universal Coefficient Theorem and let $G$ be a finitely generated discrete abelian group. Suppose $Λ: G\to Aut(A)$ is a \hm. Then $A\rtimes_Λ G$ can always be embedded into a unital simple AF-algebra. | |
| dc.identifier | https://arxiv.org/abs/math/0604047 | |
| dc.identifier | http://arxiv.org/abs/math/0604047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111426 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05, 37A55 | |
| dc.title | Embedding Crossed Products into a Unital Simple AF-algebra | |
| dc.type | text |