On Nuclearity of $C^*$-algebras of Fell bundles over \'etale groupoids
Takuya Takeishi

TL;DR
This paper proves that the nuclearity of fibers in a Fell bundle over an amenable étale groupoid implies the nuclearity of its associated $C^*$-algebra, using tensor product constructions.
Contribution
It introduces minimal tensor products of Fell bundles with fixed $C^*$-algebras to establish nuclearity transfer.
Findings
Nuclear fibers imply nuclear $C^*$-algebra for the Fell bundle
Introduces tensor product framework for Fell bundles
Establishes nuclearity preservation under certain conditions
Abstract
In this paper, we show that if E is a Fell bundle over an amenable \'etale locally compact Hausdorff groupoid such that every fiber on the unit space is nuclear, then is also nuclear. In order to show this result, we introduce (minimal) tensor products of Fell bundles with fixed -algebras.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
