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A Note on the Representation Theory of Fell Bundles

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Ruy Exel

Operator Algebras · Submitted 5 Apr 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Combining our results with those of Ng we show that if B satisfies the "approximation property" then it is amenable in the sense that the full and reduced cross-sectional C*-algebras coincide.

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arXiv IDmath/9904013 (version 1)
Pith IDI6NZIUPM, Pith's permanent record of this paper and its review
CitationRuy Exel. "A Note on the Representation Theory of Fell Bundles." arXiv:math/9904013 (1999). https://pith.science/paper/I6NZIUPM
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,288 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.81 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We show that every Fell bundle B over a locally compact group G is "proper" in a sense recently introduced by Ng. Combining our results with those of Ng we show that if B satisfies the "approximation property" then it is amenable in the sense that the full and reduced cross-sectional C*-algebras coincide.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that every Fell bundle B over a locally compact group G is "proper" in a sense recently introduced by Ng. result 0.92 0.94 0.39 asserted 1.00
s1 Combining our results with those of Ng we show that if B satisfies the "approximation property" then it is amenable in the sense that the full and reduced cross-sectional C*-algebras coincide. result 0.99 0.84 0.56 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that every Fell bundle B over a locally compact group G is "proper" in a sense recently introduced by Ng. Combining our results with those of Ng we show that if B satisfies the "approximation property" then it is amenable in the sense that the full and reduced cross-sectional C*-algebras coincide.

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