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2013 THE 2-RANKS OF CONNECTED COMPACT LIE GROUPS
Bang-Yen Chen
Taiwanese J. Math. 17(3): 815-831 (2013). DOI: 10.11650/tjm.17.2013.2606

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].

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Bang-Yen Chen. "THE 2-RANKS OF CONNECTED COMPACT LIE GROUPS." Taiwanese J. Math. 17 (3) 815 - 831, 2013. https://doi.org/10.11650/tjm.17.2013.2606

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1294.22006
MathSciNet: MR3072263
Digital Object Identifier: 10.11650/tjm.17.2013.2606

Subjects:
Primary: 22.02 , 22E40
Secondary: 22E67

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

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 3 • 2013
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