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Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals

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Le Anh Vu, Ha Van Hieu, Tran Thi Hieu Nghia

Representation Theory · Submitted 11 Jan 2011

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

The authors' main claim The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal.

how it is stated · asserted 1.00 read the record →

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arXiv ID1101.2181 (version 2)
Pith IDR4ZCOESK, Pith's permanent record of this paper and its review
CitationHa Van Hieu, Le Anh Vu, Tran Thi Hieu Nghia. "Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals." arXiv:1101.2181 (2011). https://pith.science/paper/R4ZCOESK
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,001 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e. five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbits) are orbits of zero or maximal dimension. The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal. With this result, we have the complete classification of 5-dimensional solvable Lie algebras.

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 The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e. five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbits) are orbits of zero or maximal dimension. contribution 0.82 0.71 0.04 asserted 1.00
s1 The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal. result 0.89 0.95 0.98 asserted 1.00
s2 With this result, we have the complete classification of 5-dimensional solvable Lie algebras. interpretation 0.88 0.84 0.24 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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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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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

The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e. five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbits) are orbits of zero or maximal dimension. The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal. With this result, we have the complete classification of 5-dimensional solvable Lie algebras.

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