C*-algebras associated to product systems of hilbert bimodules

By Aidan Sims, Trent Yeend. 2007

72 citations recorded by the source corpus.

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. 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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8031f01ac4c9c824fd1b236089a5784e4955a5f5

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In Algebra and Number Theory

1. Adam H. Fuller
2. E. Kakariadis
3. K. Davidson
4. Orr Shalit

In Mathematical Physics

1. Adam H. Fuller
2. E. Kakariadis
3. K. Davidson
4. Orr Shalit
5. Michael Hartz
6. Martin J. Wainwright

Citations in the corpus

• Semicrossed Products of Operator Algebras by Semigroups (2014, methodology): “, Carlsen-Larsen-Sims-Vittadello [22], Deaconu-Kumjian-Pask-Sims [38], Donsig-Katavolos-Manoussos [41], Duncan-Peters [45], Exel-Renault [47], Fowler [48], Laca [64], Larsen [68], Muhly-Solel [75], Peters [86], Sims-Yeend [90], and Solel [92, 93].”