Summary: MINIMAL E0-SEMIGROUPS
Department of Mathematics
University of California
Berkeley CA 94720, USA
6 December 1995
Abstract. It is known that every semigroup of normal completely positive maps
of a von Neumann can be "dilated" in a particular way to an E0-semigroup acting
on a larger von Neumann algebra. The E0-semigroup is not uniquely determined by
the completely positive semigroup; however, it is unique (up to conjugacy) provided
that certain conditions of minimality are met. Minimality is a subtle property, and
it is often not obvious if it is satisfied for specific examples even in the simplest case
where the von Neumann algebra is B(H).
In this paper we clarify these issues by giving a new characterization of minimality
in terms of projective cocycles and their limits. Our results are valid for semigroups
of endomorphisms acting on arbitrary von Neumann algebras with separable predual.
1991 Mathematics Subject Classification. Primary 46L40; Secondary 81E05.
Key words and phrases. von Neumann algebras, automorphism groups, E0-semigroups, mini-
This research was supported by NSF grants DMS92-43893 and DMS95-00291