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The geometric classification of nilpotent Tortkara algebras

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Ilya Gorshkov, Ivan Kaygorodov, Mykola Khrypchenko

Rings and Algebras · Submitted 5 Jun 2019

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

The authors' main claim We give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$

how it is stated · asserted 1.00 read the record →

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arXiv ID1906.02189 (version 1)
Pith ID7MG64J5N, Pith's permanent record of this paper and its review
CitationIlya Gorshkov, Ivan Kaygorodov, Mykola Khrypchenko. "The geometric classification of nilpotent Tortkara algebras." arXiv:1906.02189 (2019). https://pith.science/paper/7MG64J5N
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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, 1,593 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.59 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$

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 give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$ contribution 0.95 0.96 0.90 asserted 1.00

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

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

We give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$

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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 · 3 sentences without a confident label

Cites as background 4 papers
  • There are many results related to both the algebraic and geometric classification of small dimensional algebras in the varieties of Jordan, Lie, Leibniz and Zinbiel algebras; for algebraic results see, for example, [ref] ; for geometric results see, for example, [ref] .

    Complete classification of algebras of level two · Introduction · 0.98

  • There are many results related to both the algebraic and geometric classification of small dimensional algebras in the varieties of Jordan, Lie, Leibniz and Zinbiel algebras; for algebraic results see, for example, [ref] ; for geometric results see, for example, [ref] .

    The algebraic and geometric classification of nilpotent bicommutative algebras · Introduction · 0.98

  • There are many results related to both the algebraic and geometric classification of small dimensional algebras in the varieties of Jordan, Lie, Leibniz and Zinbiel algebras; for algebraic results see, for example, [ref] ; for geometric results see, for example, [ref] .

    The algebraic classification of nilpotent Tortkara algebras · Introduction · 0.98

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