A family of non-cocycle conjugate E_0-semigroups obtained from boundary weight doubles
Christopher Jankowski

TL;DR
This paper constructs a family of type II_0 E_0-semigroups from boundary weight doubles and classifies when they are cocycle conjugate, based on properties of the boundary maps and weights.
Contribution
It introduces a classification of non-cocycle conjugate E_0-semigroups derived from boundary weight doubles with rank one q-positive maps.
Findings
E_0-semigroups are non-cocycle conjugate if boundary maps have different eigenvalue lists.
Complete classification of q-corners and hyper maximal q-corners between boundary maps.
Cocycle conjugacy characterized by conjugacy of boundary maps and equality of dimensions.
Abstract
We have seen that if \phi: M_n(\C) \rightarrow M_n(\C) is a unital q-positive map and \nu is a type II Powers weight, then the boundary weight double (\phi, \nu) induces a unique (up to conjugacy) type II_0 E_0-semigroup. Let \phi: M_n(\C) \rightarrow M_n(\C) and \psi: M_{n'}(\C) \rightarrow M_{n'}(\C) be unital rank one q-positive maps, so for some states \rho \in M_n(\C)^* and \rho' \in M_{n'}(\C)^*, we have \phi(A)=\rho(A)I_n and \psi(D) = \rho'(D)I_{n'} for all A \in M_n(\C) and D \in M_{n'}(\C). We find that if \nu and \eta are arbitrary type II Powers weights, then (\phi, \nu) and (\psi, \eta) induce non-cocycle conjugate E_0-semigroups if \rho and \rho' have different eigenvalue lists. We then completely classify the q-corners and hyper maximal q-corners from \phi to \psi, obtaining the following result: If \nu is a type II Powers weight of the form \nu(\sqrt{I - \Lambda(1)} B…
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Operator Algebra Research · Geometric and Algebraic Topology
