Stable rank for inclusions of C*-algebras
| dc.creator | Osaka, Hiroyuki | |
| dc.date | 2007-08-30 | |
| dc.date.accessioned | 2026-07-07T08:26:36Z | |
| dc.date.available | 2026-07-07T08:26:36Z | |
| dc.description | When a unital \ca $A$ has topological stable rank one (write $\tsr(A) = 1$), we know that $\tsr(pAp) \leq 1$ for a non-zero projection $p \in A$. When, however, $\tsr(A) \geq 2$, it is generally faluse. We prove that if a unital C*-algebra $A$ has a simple unital C*-subalgebra $D$ of $A$ with common unit such that $D$ has \PSP and $\sup_{p\in P(D)}\tsr(pAp) < \infty$, then $\tsr(A) \leq 2.$ As an application let $A$ be a simple unital \ca with $\tsr(A) = 1$ and \PSP, $\{G_k\}_{k=1}^n$ finite groups, $\af_k$ actions from $G_k$ to ${\rm Aut}((...((A\times_{\af_1}G_1)\times_{\af_2} G_2)...)\times_{\af_{k-1}}G_{k-1}).$ $(G_0 = \{1\})$ Then $$ \tsr((... ((A\times_{\af_1}G_1)\times_{\af_2} G_2)...)\times_{\af_n}G_n) \leq 2. $$ | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0708.4045 | |
| dc.identifier | http://arxiv.org/abs/0708.4045 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136996 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05 | |
| dc.title | Stable rank for inclusions of C*-algebras | |
| dc.type | text |