Taiwanese Journal of Mathematics

THE 2-RANKS OF CONNECTED COMPACT LIE GROUPS

Bang-Yen Chen

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Abstract

The 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times\cdots {\mathbb Z}_{2}$ 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 [9]. 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 maximal antipodal sets $A_{2}G$ of $G$ introduced in [16, 17].

Article information

Source
Taiwanese J. Math., Volume 17, Number 3 (2013), 815-831.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705985

Digital Object Identifier
doi:10.11650/tjm.17.2013.2606

Mathematical Reviews number (MathSciNet)
MR3072263

Zentralblatt MATH identifier
1294.22006

Subjects
Primary: 22.02 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05]

Keywords
2-rank 2-subgroup 2-number compact Lie group antipodal set $(M_{+},M_{-})$-method

Citation

Chen, Bang-Yen. THE 2-RANKS OF CONNECTED COMPACT LIE GROUPS. Taiwanese J. Math. 17 (2013), no. 3, 815--831. doi:10.11650/tjm.17.2013.2606. https://projecteuclid.org/euclid.twjm/1499705985


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