Archive - Keywords property SP

Let \(1 \in A \subset B\) be an inclusion of unital \(C^*\)-algebras of index-finite type and depth \(2\). Suppose that \(A\) is infinite dimensional, simple, with the property \(\operatorname{SP}\). We prove that if \(\operatorname{tsr}(A) = 1\), then \(\operatorname{tsr}(B) \leq 2\). An interesting special case is \(B = A \rtimes_\alpha G\), where \(\alpha\) is an action of a finite group \(G\) on \(\operatorname{Aut}(A)\).

Soit \(1 \in A \subset B\) une inclusion de \(C^*\)-algèbres unitals du type indice-fini et de profondeur \(2\). On suppose que \(A\) est de dimension infinie, simple, et que \(A\) a la propriété \(\operatorname{SP}\). On démontre que, si \(\operatorname{tsr}(A) = 1\), donc \(\operatorname{tsr}(B) \leq 2\). Un cas intéressant est \(B = A \rtimes_\alpha G\), oú \(\alpha\) est une action d’un groupe fini \(G\) sur \(\operatorname{Aut}(A)\).