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Boundary rigidity for free product C*-algebras

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Kei Hasegawa

Operator Algebras · Submitted 28 Aug 2017

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

The authors' main claim For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A, \varphi)$.

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arXiv ID1708.08260 (version 1)
Pith ID4KMWTZKZ, Pith's permanent record of this paper and its review
CitationKei Hasegawa. "Boundary rigidity for free product C*-algebras." arXiv:1708.08260 (2017). https://pith.science/paper/4KMWTZKZ
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The compiled record

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,469 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.15 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A, \varphi)$. This provides new examples of rigid embeddings of exact $\mathrm{C}^*$-algebras into purely infinite simple nuclear $\mathrm{C}^*$-algebras.

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 For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A, \varphi)$. result 0.72 0.96 0.89 asserted 1.00
s1 This provides new examples of rigid embeddings of exact $\mathrm{C}^*$-algebras into purely infinite simple nuclear $\mathrm{C}^*$-algebras. interpretation 0.86 0.85 0.20 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · 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

For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A, \varphi)$. This provides new examples of rigid embeddings of exact $\mathrm{C}^*$-algebras into purely infinite simple nuclear $\mathrm{C}^*$-algebras.

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