Continuous families of E_0-semigroups

TL;DR

This paper studies continuous families of E_0-semigroups parametrized by compact spaces, establishing a correspondence with principal bundles when the gauge group is a Lie group, thus linking operator algebraic structures with geometric objects.

Contribution

It introduces a classification of continuous families of E_0-semigroups via principal bundles, extending the understanding of their structure when the gauge group is a Lie group.

Findings

Continuous families correspond to principal bundles with gauge group as structure group.

Established a bijective correspondence between families and principal bundles.

Extended the classification framework for E_0-semigroups in the context of Lie gauge groups.

Abstract

We consider families of E_0-semigroups continuously parametrized by a compact Hausdorff space, which are cocycle-equivalent to a given E_0-semigroup \beta. When the gauge group of $\beta$ is a Lie group, we establish a correspondence between such families and principal bundles whose structure group is the gauge group of \beta.