Renault's $j$-map for Fell bundle $C^*$-algebras
Anna Duwenig, Dana P. Williams, Joel Zimmerman

TL;DR
This paper introduces a new injective linear map called the $j$-map for Fell bundle $C^*$-algebras over étale groupoids, generalizing a classical map in the theory of groupoid $C^*$-algebras.
Contribution
It constructs a norm reducing injective linear map from reduced Fell bundle $C^*$-algebras to sections, extending known results for groupoid $C^*$-algebras.
Findings
The $j$-map is norm reducing and injective.
Generalizes the classical $j$-map for groupoid $C^*$-algebras.
Provides a new tool for analyzing Fell bundle $C^*$-algebras.
Abstract
If is a Fell bundle over an \'etale groupoid, then we show that there is an norm reducing injective linear map generalizing the well know map in the case of an \'etale groupoid.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
