On the decomposition of an (L)-group

Yozô MATSUSHIMA

doi:10.2969/jmsj/00140264

Yozô MATSUSHIMA

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ジャーナルフリー

1950 年 1 巻 4 号 p. 264-274

DOI https://doi.org/10.2969/jmsj/00140264

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Published: 1950 Received: 1949/02/15 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
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訂正日: 2006/08/29 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Yozo MATSUSHIMA¹⁾
Right : Yozô MATSUSHIMA¹⁾

訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Right : 1) For (L)-groups, see K. Iwasawa. On some types of topological groups, Annals of Math. Vol. 50, No. 3 (1949). We shall refer to this paper as I.
2) For Levi's theorem, see J. H. C. Whitehead. On the decomposition of an infinitesimal group, Proc. Cambr. Phil. Soc. v. 32. (1932), A. Malcev. On the representation of an algebra as a direct sum of the radical and a semi-simple algebra, C. R. DRSS, 36 (1942) and M. Gotô, On a theorem of E. E. Levi, Mathematica Japonicae. Vol. 1. No. 3 (1949).
3) See, I.
4) M. Gotô, Linear representations of topological groups, to appear shortly. We shall refer to this paper as G.
5) L is the component of the unit element in the centraliser of C.
6) See, G.
7) See, G.
8) H. Weyl, Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen, I-III, Math. Zeit. Bd. 23-24 (1924-25).
9) See, I.
10) See, A. Malcev, loc. cit.
11) See, G.
12) For, by I, maximal compact subgroups are conjugate with each other and any compact abelian normal subgroup is contained in the center of G.
13) See, I. Lemma 4.8
14) See, H. Freudenthal, Topologische Gruppen mit genügend vielen fastperiodischen Funktionen, Ann. of Math. 37 (1936).
15) See, G.
16) See, G.
17) For the definition and properties of (l)-groups, see, G.
18) A Lie group is said to be faithfully representable, if it admits an isomorphic continuous representaion by matrices.
19) K. Yosida, A theorem concerning the semi-simple Lie groups, Tohoku Math. Journ. v. 43 (1937).

訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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