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.
Journal of Operator Theory Vol. 64, Issue 2, p. 349-376