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Hopf algebras of prime dimension in positive characteristic

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Siu-Hung Ng, Xingting Wang

Quantum Algebra · Submitted 30 Sep 2018

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

The authors' main claim We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra.

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arXiv ID1810.00476 (version 3)
Pith ID6IY2T6UJ, Pith's permanent record of this paper and its review
CitationSiu-Hung Ng, Xingting Wang. "Hopf algebras of prime dimension in positive characteristic." arXiv:1810.00476 (2018). https://pith.science/paper/6IY2T6UJ
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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, 2,978 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.19 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of prime dimension $p$ over a field of characteristic $q>0$ is commutative and cocommutative when $q=2$ or $p<4q$. This problem remains open in positive characteristic when $2<q<p/4$.

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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 We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. result 0.95 0.96 0.80 asserted 1.00
s1 Moreover, we show that any Hopf algebra of prime dimension $p$ over a field of characteristic $q>0$ is commutative and cocommutative when $q=2$ or $p<4q$. result 0.98 0.93 0.14 asserted 1.00
s2 This problem remains open in positive characteristic when $2<q<p/4$. gap 0.47 0.09 0.03 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · 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

We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of prime dimension $p$ over a field of characteristic $q>0$ is commutative and cocommutative when $q=2$ or $p<4q$. This problem remains open in positive characteristic when $2<q<p/4$.

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4 arXiv papers cite this in 10 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

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