Iterating the Pimsner construction
| dc.creator | Deaconu, Valentin | |
| dc.date | 2007-07-11 | |
| dc.date.accessioned | 2026-07-07T08:16:11Z | |
| dc.date.available | 2026-07-07T08:16:11Z | |
| dc.description | For $A$ a $C^*$-algebra, $E_1, E_2$ two Hilbert bimodules over $A$, and a fixed isomorphism $χ: E_1\otimes_AE_2\to E_2\otimes_AE_1$, we consider the problem of computing the $K$-theory of the Cuntz-Pimsner algebra ${\mathcal O}_{E_2\otimes_A{\mathcal O}_{E_1}}$ obtained by extending the scalars and by iterating the Pimsner construction. The motivating examples are a commutative diagram of Douglas and Howe for the Toeplitz operators on the quarter plane, and the Toeplitz extensions associated by Pimsner and Voiculescu to compute the $K$-theory of a crossed product. The applications are for Hilbert bimodules arising from rank two graphs and from commuting endomorphisms of abelian $C^*$-algebras. | |
| dc.identifier | https://arxiv.org/abs/0707.1710 | |
| dc.identifier | http://arxiv.org/abs/0707.1710 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133695 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05 (Primary); 46L55, 46L80 (Secondary) | |
| dc.title | Iterating the Pimsner construction | |
| dc.type | text |