Distinguishing C*-algebras by their unitary groups

Leonel Robert; Lionel Fogang Takoutsing

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Distinguishing C*-algebras by their unitary groups

Operator Algebras · Submitted 27 Jun 2023

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

The authors' main claim We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

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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, 1,682 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.89 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real 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.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C-algebras, either as topological groups or as discrete groups, implies isomorphism of the C-algebras as real C*-algebras.	result 0.78	0.92	0.82	asserted 0.84

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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arXiv listing abstract v1

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figures and tables
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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 obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

For another recent work related to unitary groups of $C^*$-algebras from the Lie perspective, we refer e.g., to [ref] .

Lie theoretic approach to unitary groups of $C^*$-algebras · Introduction · 0.99

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