THE 2-RANKS OF CONNECTED COMPACT LIE GROUPS

The 2-rank of a compact Lie groupGis the maximal possible rank of the elementary 2-subgroup ℤ2×⋯ℤ2ofG. The study of 2-ranks (andp-rank for any primep) 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 m...

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Published inTaiwanese journal of mathematics Vol. 17; no. 3; pp. 815 - 831
Main Author Chen, Bang-Yen
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2013
Subjects
Algebra
Lie groups
Logical theorems
Mathematical theorems
Morphisms
Prime numbers
Symmetry
Topological compactness
Topological theorems
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Summary:The 2-rank of a compact Lie groupGis the maximal possible rank of the elementary 2-subgroup ℤ2×⋯ℤ2ofG. The study of 2-ranks (andp-rank for any primep) 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 groupsGvia the maximal antipodal setsA 2 GofGintroduced in [16, 17]. 2010Mathematics Subject Classification: Primary 22.02, 22E40; Secondary 22E67. Key words and phrases: 2-Rank, 2-Subgroup, 2-Number, Compact Lie group, Antipodal set, (M +,M− )-Method.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.2606