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Leibniz algebroid associated with a Nambu-Poisson structure

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R. Ibanez (University of the Basque Country), M. de Leon (C.S.I.C.), J. C. Marrero (University of La Laguna), E. Padron (University of La Laguna)

Mathematical Physics · Submitted 30 Jun 1999

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

The authors' main claim The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath-ph/9906027 (version 1)
Pith ID77G5L46K, Pith's permanent record of this paper and its review
CitationE. Padron (University of La Laguna), J. C. Marrero (University of La Laguna), M. de Leon (C.S.I.C.), R. Ibanez (University of the Basque Country). "Leibniz algebroid associated with a Nambu-Poisson structure." arXiv:math-ph/9906027 (1999). https://pith.science/paper/77G5L46K
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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, 2,315 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.55 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds.

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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 notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. contribution 0.76 0.89 0.61 asserted 1.00
s1 This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds. interpretation 0.46 0.81 0.33 asserted 0.96

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

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  • C citations
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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

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds.

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3 arXiv papers cite this in 5 sentences

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

Papers citing it · 1 sentence without a confident label

Cites it as background 2 papers
  • In this paper, we focus on the interplay between Lie–Rinehart algebras [ref] (Lie algebroids [ref] in a differential geometric context) and Leibniz algebroids [ref] which are generalisations of Lie algebras and Leibniz algebras respectively.

    Lie Algebroids in the Loday-Pirashvili Category · Introduction · 0.99

  • The modular classes of Leibniz algebroids [ref] , of Nambu–Poisson structures [ref] , of Jacobi manifolds [ref] and Jacobi algebroids (also called generalized Lie algebroids) [ref] have been defined, their unimodularity implying a homology/cohomology duality, as well as those of symp­lectic supermanifolds [ref] .

    Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey · Appendix: additional references and conclusion · 0.87

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