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Crossed product C*-algebras by finite group actions with the projection free tracial Rokhlin property

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Dawn Archey

Operator Algebras · Submitted 19 Feb 2009

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

The authors' main claim Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^*$-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if $\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^*(G, A, \alpha)$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven)

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arXiv ID0902.3324 (version 2)
Pith IDYIVDE555, Pith's permanent record of this paper and its review
CitationDawn Archey. "Crossed product C*-algebras by finite group actions with the projection free tracial Rokhlin property." arXiv:0902.3324 (2009). https://pith.science/paper/YIVDE555
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,527 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.97 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections. Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^*$-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if $\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^*(G, A, \alpha)$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven)

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 In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections. contribution 1.00 0.94 0.05 asserted 0.98
s1 Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^*$-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if $\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^*(G, A, \alpha)$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven) result 0.78 0.83 0.79 asserted 0.95

What kind of paper the classifier reports this is: theoretical result 0.60 · evidence from proof or derivation 0.99.

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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

In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections. Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^*$-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if $\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^*(G, A, \alpha)$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven)

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