Curve selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups |
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Authors: | An JinPeng Wang ZhengDong |
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Affiliation: | (1) School of Mathematical Sciences, Peking University, Beijing, 100871, China |
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Abstract: | 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. |
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Keywords: | semianalytic set Curve Selection Lemma Lie group conjugacy class |
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