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Higher-rank graph C*-algebras: an inverse semigroup and groupoid approach

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Cynthia Farthing, Paul S. Muhly, Trent Yeend

Operator Algebras · Submitted 27 Sep 2004

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

The authors' main claim Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.

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arXiv IDmath/0409505 (version 3)
Pith IDU6CJIHYD, Pith's permanent record of this paper and its review
CitationCynthia Farthing, Paul S. Muhly, Trent Yeend. "Higher-rank graph C*-algebras: an inverse semigroup and groupoid approach." arXiv:math/0409505 (2004). https://pith.science/paper/U6CJIHYD
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,255 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; .

We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.

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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 provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. contribution 0.82 0.95 0.21 asserted 1.00
s1 Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra. result 0.87 0.96 0.58 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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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 provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.

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