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Low dimensional matrix representations for noncommutative surfaces of arbitrary genus

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Joakim Arnlind

Representation Theory · Submitted 14 Jan 2019

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

The authors' main claim The existence of representations crucially depends on the analytic structure of the polynomial defining the surface as a level set in $\mathbb{R}^3$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1901.04270 (version 2)
Pith IDMC72WNYC, Pith's permanent record of this paper and its review
CitationJoakim Arnlind. "Low dimensional matrix representations for noncommutative surfaces of arbitrary genus." arXiv:1901.04270 (2019). https://pith.science/paper/MC72WNYC
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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, 3,586 input tokens.

What the abstract itself states, as probabilities: claims first 0.31 · states limitation 0.65 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.35 · compares with prior results 0.05 · 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 note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. In particular, for arbitrary genus greater than one, we explicitly construct classes of irreducible two and three dimensional representations. The existence of representations crucially depends on the analytic structure of the polynomial defining the surface as a level set in $\mathbb{R}^3$.

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 note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. contribution 0.99 0.88 0.09 asserted 0.96
s1 Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. method 0.92 0.91 0.09 asserted 1.00
s2 In particular, for arbitrary genus greater than one, we explicitly construct classes of irreducible two and three dimensional representations. result 0.73 0.95 0.44 asserted 1.00
s3 The existence of representations crucially depends on the analytic structure of the polynomial defining the surface as a level set in $\mathbb{R}^3$. result 0.89 0.65 0.25 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 v2
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

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. In particular, for arbitrary genus greater than one, we explicitly construct classes of irreducible two and three dimensional representations. The existence of representations crucially depends on the analytic structure of the polynomial defining the surface as a level set in $\mathbb{R}^3$.

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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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