 

Valentin Deaconu
Iterating the Pimsner construction


Published: 
July 17, 2007

Keywords: 
C*algebra, Hilbert bimodule, Ktheory 
Subject: 
Primary 46L05; Secondary 46L55, 46L80 


Abstract
For A a C*algebra, E_{1}, E_{2} two Hilbert bimodules over A, and a fixed isomorphism ϗ : E_{1}⊗_{A}E_{2}→ E_{2}⊗_{A}E_{1}, we consider the problem of computing the Ktheory of the CuntzPimsner algebra O_{E2⊗AO}_{E1} 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 Ktheory of a crossed product. The applications are for Hilbert bimodules arising from rank two graphs and from commuting endomorphisms of abelian C*algebras.


Author information
Department of Mathematics and Statistics, University of Nevada, Reno NV 895570084, USA
vdeaconu@unr.edu

