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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.

UOW Authors


Publication Date


  • 2010

Citation


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

Scopus Eid


  • 2-s2.0-78049286277

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3460

Number Of Pages


  • 27

Start Page


  • 349

End Page


  • 376

Volume


  • 64

Issue


  • 2

Place Of Publication


  • http://www.theta.ro/jot/archive/2010-064-002/2010-064-002-005.html

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.

UOW Authors


Publication Date


  • 2010

Citation


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

Scopus Eid


  • 2-s2.0-78049286277

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3460

Number Of Pages


  • 27

Start Page


  • 349

End Page


  • 376

Volume


  • 64

Issue


  • 2

Place Of Publication


  • http://www.theta.ro/jot/archive/2010-064-002/2010-064-002-005.html