Compactly-aligned discrete product systems, and generalizations of O_\infty

Details Compactly-aligned discrete product systems, and generalizations of O_\infty Compactly-aligned discrete product systems, and generalizations of O_\infty

1998-09-29

arxiv.org/abs/math/9809181v1

Mathematics

Operator Algebras

AMS-LaTeX, 17 pages

Scientific paper

The universal C*-algebras of discrete product systems generalize the Toeplitz- Cuntz algebras and the Toeplitz algebras of discrete semigroups. We consider a semigroup P which is quasi-lattice ordered in the sense of Nica, and, for a product system p:E\to P, we study those representations of E, called covariant, which respect the lattice structure of P. We identify a class of product systems, which we call compactly aligned, for which there is a purely C*-algebraic characterization of covariance, and study the algebra C*_{cov}(P,E) which is universal for covariant representations of E. Our main theorem is a characterization of the faithful representations of C*_{cov}(P,E) when P is the positive cone of a free product of totally-ordered amenable groups.

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