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Differential projective modules over algebras with radical square zero

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Dawei Shen

Representation Theory · Submitted 31 Mar 2018

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

The authors' main claim We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations of the opposite of $Q$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1804.00169 (version 1)
Pith IDPOR2AR2H, Pith's permanent record of this paper and its review
CitationDawei Shen. "Differential projective modules over algebras with radical square zero." arXiv:1804.00169 (2018). https://pith.science/paper/POR2AR2H
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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, 2,956 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations of the opposite of $Q$. If moreover $Q$ has oriented cycles and $Q$ is not a basic cycle, we prove that the algebra of dual numbers over $\Lambda$ is not virtually Gorenstein.

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 Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. background 1.00 0.10 0.02 asserted 0.83
s1 We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations of the opposite of $Q$. contribution 0.64 0.96 0.57 asserted 1.00
s2 If moreover $Q$ has oriented cycles and $Q$ is not a basic cycle, we prove that the algebra of dual numbers over $\Lambda$ is not virtually Gorenstein. result 0.99 0.93 0.31 asserted 1.00

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

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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

Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations of the opposite of $Q$. If moreover $Q$ has oriented cycles and $Q$ is not a basic cycle, we prove that the algebra of dual numbers over $\Lambda$ is not virtually Gorenstein.

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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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