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A CLASS OF ESSENTIAL REPRESENTATIONS OF PRODUCT SYSTEMS
 

Summary: A CLASS OF ESSENTIAL REPRESENTATIONS OF
PRODUCT SYSTEMS
REMUS FLORICEL
Abstract. We construct a family of essential representations of
an arbitrary product system by generalizing some techniques intro-
duced 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.
1. Introduction
The study of product systems and E0-semigroups occupies a cen-
tral place in the theory of noncommutative dynamics [6]. One of the
most important problems in this subject is arguably to provide explicit
constructions of essential representations of arbitrary product systems,
and to classify the resulting E0-semigroups.

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics