Curve selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group G , each connected component of the set E n ( G ) of all elements of order n in G is a conjugacy class in G . In particular, all conjugacy classes of finite order in G a...

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Bibliographic Details
Published inScience in China. Series A, Mathematics, physics, astronomy Vol. 51; no. 3; pp. 383 - 388
Main Authors An, JinPeng, Wang, ZhengDong
Format Journal Article
LanguageEnglish
Published Beijing Science in China Press 01.03.2008
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
semianalytic set
22E15
Curve Selection Lemma
conjugacy class
Lie group
14P15
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Summary:Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group G , each connected component of the set E n ( G ) of all elements of order n in G is a conjugacy class in G . In particular, all conjugacy classes of finite order in G are closed. Some properties of connected components of E n ( G ) are also given.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1006-9283
1862-2763
DOI:10.1007/s11425-007-0185-2