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The 2-ranks of connected compact Lie groups

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Bang-Yen Chen

Group Theory · Submitted 8 Jul 2013

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

The authors' main claim In particular, we present the complete determination of 2-ranks of compact connected simple Lie groups $G$ via the 2-numbers introduced by B. Y. Chen and T.

how it is stated · asserted 1.00 read the record →

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arXiv ID1307.1932 (version 1)
Pith ID53KBOEUI, Pith's permanent record of this paper and its review
CitationBang-Yen Chen. "The 2-ranks of connected compact Lie groups." arXiv:1307.1932 (2013). https://pith.science/paper/53KBOEUI
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,940 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. The study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was initiated in 1953 by A. Borel and J.-P. Serre. Since then the 2-ranks of compact Lie groups have been investigated by many mathematician. The 2-ranks of compact Lie groups relate closely with several important areas in mathematics. In this article, we survey important results concerning 2-ranks of compact Lie groups. In particular, we present the complete determination of 2-ranks of compact connected simple Lie groups $G$ via the 2-numbers introduced by B. Y. Chen and T. Nagano in [Un invariant g\'em\'etrique riemannien, C. R. Acad. Sci. Paris, 295 (1982), 389--391] and [A Riemannian geometric invariant and its applications to a problem of Borel and Serre, Trans. Amer. Math. Soc. 308 (1988), 273--297].

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 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. background 1.00 0.06 0.03 asserted 1.00
s1 The study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was initiated in 1953 by A. Borel and J.-P. Serre. background 1.00 0.03 0.02 asserted 1.00
s2 Since then the 2-ranks of compact Lie groups have been investigated by many mathematician. background 1.00 0.03 0.02 asserted 1.00
s3 The 2-ranks of compact Lie groups relate closely with several important areas in mathematics. background 0.99 0.05 0.03 asserted 1.00
s4 In this article, we survey important results concerning 2-ranks of compact Lie groups. contribution 1.00 0.65 0.13 asserted 0.97
s5 In particular, we present the complete determination of 2-ranks of compact connected simple Lie groups $G$ via the 2-numbers introduced by B. Y. Chen and T. contribution 0.76 0.74 0.73 asserted 1.00
s6 Nagano in [Un invariant g\'em\'etrique riemannien, C. R. Acad. background 0.62 0.04 0.02 unclear 0.98
s7 Sci. Paris, 295 (1982), 389--391] and [A Riemannian geometric invariant and its applications to a problem of Borel and Serre, Trans. Amer. Math. background 0.77 0.05 0.02 unclear 0.96
s8 Soc. 308 (1988), 273--297]. background 0.80 0.04 0.02 unclear 0.98

What kind of paper the classifier reports this is: review 0.99 · evidence from literature 0.98.

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
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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 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. The study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was initiated in 1953 by A. Borel and J.-P. Serre. Since then the 2-ranks of compact Lie groups have been investigated by many mathematician. The 2-ranks of compact Lie groups relate closely with several important areas in mathematics. In this article, we survey important results concerning 2-ranks of compact Lie groups. In particular, we present the complete determination of 2-ranks of compact connected simple Lie groups $G$ via the 2-numbers introduced by B. Y. Chen and T. Nagano in [Un invariant g\'em\'etrique riemannien, C. R. Acad. Sci. Paris, 295 (1982), 389--391] and [A Riemannian geometric invariant and its applications to a problem of Borel and Serre, Trans. Amer. Math. Soc. 308 (1988), 273--297].

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