New York Journal of Mathematics
Volume 13 (2007) 199-213


Valentin Deaconu

Iterating the Pimsner construction

Published: July 17, 2007
Keywords: C*-algebra, Hilbert bimodule, K-theory
Subject: Primary 46L05; Secondary 46L55, 46L80

For A a C*-algebra, E1, E2 two Hilbert bimodules over A, and a fixed isomorphism ϗ : E1AE2→ E2AE1, we consider the problem of computing the K-theory of the Cuntz-Pimsner algebra OE2AOE1 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.

Author information

Department of Mathematics and Statistics, University of Nevada, Reno NV 89557-0084, USA