C*-algebras associated to product systems of Hilbert bimodules

Aidan Sims*, Trent Yeend

*Corresponding author for this work

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)349-376
Number of pages28
JournalJournal of Operator Theory
Volume64
Issue number2
Publication statusPublished - Sep 2010
Externally publishedYes

Keywords

  • Cuntz-pimsner algebra
  • Hilbert bimodule

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