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Coordinates for non-integrable Lie algebroids

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Iakovos Androulidakis

Differential Geometry · Submitted 22 Jun 2021

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

The authors' main claim We construct local coordinates for the Weinstein groupoid of a non-integrable Lie algebroid.

how it is stated · asserted 1.00 read the record →

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arXiv ID2106.12002 (version 1)
Pith IDZ6FBD5PF, Pith's permanent record of this paper and its review
CitationIakovos Androulidakis. "Coordinates for non-integrable Lie algebroids." arXiv:2106.12002 (2021). https://pith.science/paper/Z6FBD5PF
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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, 2,905 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We construct local coordinates for the Weinstein groupoid of a non-integrable Lie algebroid. To this end, we reformulate the notion of bi-submersion in a completely algebraic way and prove the existence of bi-submersions as such for the Weinstein groupoid. This implies that a $C^*$-algebra can be attached to every Lie algebroid.

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 We construct local coordinates for the Weinstein groupoid of a non-integrable Lie algebroid. contribution 0.95 0.95 0.64 asserted 1.00
s1 To this end, we reformulate the notion of bi-submersion in a completely algebraic way and prove the existence of bi-submersions as such for the Weinstein groupoid. method 0.93 0.95 0.09 asserted 1.00
s2 This implies that a $C^*$-algebra can be attached to every Lie algebroid. interpretation 0.91 0.74 0.34 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • P abstract
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  • 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

We construct local coordinates for the Weinstein groupoid of a non-integrable Lie algebroid. To this end, we reformulate the notion of bi-submersion in a completely algebraic way and prove the existence of bi-submersions as such for the Weinstein groupoid. This implies that a $C^*$-algebra can be attached to every Lie algebroid.

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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

What it cites · 16 sentences without a confident label

Builds on 1 paper
  • The purpose of this section is to extend the formulation of bi-submersions we gave in definition [ref] to the bi-submersions of an integrable Lie algebroid introduced in [ref] .

    Singular subalgebroids · Bi-submersions of an integrable Lie algebroid · 0.99

Cites as background 1 paper
  • Recall [ref] that if $(U,ψ,)$ is a bi-submersion of $A$ in the sense of Dfn.

    Singular subalgebroids · Reformulating the notion of bi-submersion for $A$ · 0.82

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