A class of essential representations of product systems

We construct a family of essential representations of an arbitrary product system by generalizing some techniques introduced by M. Skeide and W. Arveson. We then classify the resulting E0-semigroups up to conjugacy, by identifying their tail flows as periodic W∗-dynamical systems acting on factors of type I∞. The conjugacy classes of these E0-semigroups correspond to the orbits of the action of the automorphism group of the product system on unital vectors. In the sequel, this classification shows explicitly that any E0-semigroup admits uncountably many non-conjugate cocycle perturbations. © 2008 Elsevier Inc. All rights reserved.