C*-algebras associated to product systems of Hilbert Bimodules

Title: C*-algebras associated to product systems of Hilbert Bimodules
Creator: Sims, Aidan; Yeend, Trent
Relation: Journal of Operator Theory Vol. 64, Issue 2, p. 349-376
Relation: http://www.theta.ro/jot/archive/2010-064-002/2010-064-002-005.html
Publisher: Academia Romana
Resource Type: journal article
Date: 2010
Description: Let (G, P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules in the sense of Fowler. Under mild hypotheses we associate to X a C*-algebra which we call the Cuntz–Nica–Pimsner algebra of X. Our construction generalises a number of others: a sub-class of Fowler’s Cuntz–Pimsner algebras for product systems of Hilbert bimodules; Katsura’s formulation of Cuntz–Pimsner algebras of Hilbert bimodules; the C*-algebras of finitely aligned higher-rank graphs; and Crisp and Laca’s boundary quotients of Toeplitz algebras. We show that for a large class of product systems X, the universal representation of X in its Cuntz–Nica–Pimsner algebra is isometric.
Subject: Cuntz–Pimsner algebra; Hilbert bimodule
Identifier: http://hdl.handle.net/1959.13/928833
Identifier: uon:10456
Identifier: ISSN:0379-4024
Language: eng
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