On the decomposition of an (L)-group

Yozô MATSUSHIMA

doi:10.2969/jmsj/00140264

Yozô MATSUSHIMA

Author information

JOURNAL FREE ACCESS

1950 Volume 1 Issue 4 Pages 264-274

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

Details

Published: 1950 Received: February 15, 1949 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: August 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Yozo MATSUSHIMA¹⁾
Right : Yozô MATSUSHIMA¹⁾

Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: 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).

Date of correction: August 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!