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C*-algebras associated to product systems of hilbert bimodules

Journal Article


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. © Copyright by THETA, 2010.

Publication Date


  • 2010

Citation


  • Sims, A., & Yeend, T. (2010). C*-algebras associated to product systems of hilbert bimodules. Journal of Operator Theory, 64(2), 349-376.

Scopus Eid


  • 2-s2.0-78049286277

Web Of Science Accession Number


Start Page


  • 349

End Page


  • 376

Volume


  • 64

Issue


  • 2

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. © Copyright by THETA, 2010.

Publication Date


  • 2010

Citation


  • Sims, A., & Yeend, T. (2010). C*-algebras associated to product systems of hilbert bimodules. Journal of Operator Theory, 64(2), 349-376.

Scopus Eid


  • 2-s2.0-78049286277

Web Of Science Accession Number


Start Page


  • 349

End Page


  • 376

Volume


  • 64

Issue


  • 2