property SP — 2 results found.
C. R. Math. Rep. Acad. Sci. Canada Vol. 29 (3) 2007, pp. 81–86
Toan M. Ho (Received: 2007/08/02) C. R. Math. Rep. Acad. Sci. Canada Vol. 29 (1) 2007, pp. 28–32
Hiroyuki Osaka; Tamotsu Teruya (Received: 2006/07/11)

Mathematical Reports - Comptes rendus mathématiques
of the Academy of Science | de l'Académie des sciences
A certain non-zero projection in a simple AH algebra with diagonal morphisms between the building blocks in its inductive limit decomposition is constructed and used to prove that this algebra has the property SP.
On construit une projection convenable dans une certaine algèbre AH simple, et on l’utilise pour montrer que cette algèbre a la propriété 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 \(\operatorname{Aut}(A)\).