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Self-injective algebras under derived equivalences

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Changchang Xi, Jin Zhang

Representation Theory · Submitted 6 Oct 2023

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

The authors' main claim The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate.

how it is stated · asserted 1.00 read the record →

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arXiv ID2310.04012 (version 3)
Pith IDOLRANHTT, Pith's permanent record of this paper and its review
CitationChangchang Xi, Jin Zhang. "Self-injective algebras under derived equivalences." arXiv:2310.04012 (2023). https://pith.science/paper/OLRANHTT
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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, 2,262 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.72 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an arbitrary field are preserved under derived equivalences.

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 The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. result 0.99 0.66 0.72 asserted 1.00
s1 A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an arbitrary field are preserved under derived equivalences. contribution 0.90 0.88 0.19 asserted 1.00

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

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an arbitrary field are preserved under derived equivalences.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

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

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