We introduce a new construction of $E_0$-semigroups, called generalized CCR
flows, with two kinds of descriptions: those arising from sum systems and those
arising from pairs of $C_0$-semigroups. We get a new necessary and sufficient
condition for them to be of type III, when the associated sum system is of
finite index. Using this criterion, we construct examples of type III
$E_0$-semigroups, which can not be distinguished from $E_0$-semigroups of type
I by the invariants introduced by Boris Tsirelson. Finally, by considering the
local von Neumann algebras, and by associating a type III factor to a given
type III $E_0$-semigroup, we show that there exist uncountably many type III
$E_0$-semigroups in this family, which are mutually non-cocycle conjugate.Comment: 45 page
In this paper, we study E-semigroups over convex cones. We prove a structure theorem for E-semigroups which leave the algebra of compact operators invariant. Then we study in detail the CCR flows, E0-semigroups constructed from isometric representations, by describing their units and gauge groups. We exhibit an uncountable family of 2-parameter CCR flows, containing mutually non-cocycle-conjugate E0-semigroups.
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