Abstract

Let (G, P) be a quasilattice 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 CuntzNicaPimsner algebra of X. Our construction generalises a number of others: a subclass of Fowler's CuntzPimsner algebras for product systems of Hilbert bimodules; Katsura's formulation of CuntzPimsner algebras of Hilbert bimodules; the C*algebras of finitely aligned higherrank 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 CuntzNicaPimsner algebra is isometric. © Copyright by THETA, 2010.