K-theory of C*-algebras arising from commuting Hilbert bimodules and invariant ideals
Abstract
We study the K-theory of the Cuntz-Nica-Pimsner C∗-algebra of a rank-two product system that is an extension determined by an invariant ideal of the coefficient algebra. We use a construction of Deaconu and Fletcher that describes the Cuntz-Nica-Pimsner C∗-algebra of the product system in terms of two iterations of Pimsner's original construction of a C∗-algebra from a right-Hilbert bimodule. We apply our results to the product system built from two commuting surjective local homeomorphisms of a totally disconnected space, where the Cuntz-Nica-Pimsner C∗-algebra is isomorphic to the C∗-algebra of the associated rank-two Deaconu-Renault groupoid. We then apply a theorem of Spielberg about stable finiteness of an extension to obtain sufficient conditions for stable finiteness of the C∗-algebra of the Deaconu-Renault groupoid.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Banach Space Theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- Journal of Operator Theory
- Publisher
- Theta Foundation
- Volume
- 96
- Issue
- 1
- Pages
- 215–256
- Publication date
- 8 August 2026
- Language
- EN