Continuous families of E_0-semigroups
Ilan Hirshberg, Daniel Markiewicz

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 is a Lie group, we establish a correspondence between such families and principal bundles whose structure group is the gauge group of \beta.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis
