Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-16T19:48:22.173Z Has data issue: false hasContentIssue false
  • English
  • Français

On pro-reductive groups

Published online by Cambridge University Press:  24 October 2008

Martin Moskowitz
Martin Moskowitz
Affiliation:
The Graduate School of the City University of New York, 33 West 42 Street, New York, N.Y. 10036
Get access Rights & Permissions [Opens in a new window]

Extract

In the proof of the Freudenthal–Weil theorem in, for example (5), essential use is made of the fact that if G and H are compact analytic groups and ø: G → H is a continuous epimorphism then ø(Z(G)0) = Z(H)0 where the subscript 0 denotes the identity component of a topological group G and Z(G) its centre. Although this is sufficient for the proof of the Freudenthal–Weil theorem it raises the interesting question as to whether actually ø(Z(G)) = Z(H) (from which the above would follow) and, if so, in what generality this can be expected. The present paper deals with this question, in more general form, as well as certain of its structural consequences.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 2 , September 1974 , pp. 401 - 406
Copyright
Copyright © Cambridge Philosophical Society 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bourbaki, N.Éléments de Mathematique, Livre 7, ChapaItre 1, Groupes et Algèbres do Lie (Hermann; Paris, 1960.)Google Scholar
(2)Grosser, S. and Moskowitz, M.On central topological groups. Trans. Amer. Math. Soc. 127 (1967), 317–340.CrossRefGoogle Scholar
(3)Grosser, S., Loos, O. and Moskowitz, M.Über Automorphismengruppen lokal-kompakter Gruppen und Derivationen von Lie–Gruppen, Math. Z. 114 (1970), 321–339.CrossRefGoogle Scholar
(4)Hewitt, E. and Ross, K.Abstract harmonic analysis, vol. I (Springer; Berlin–Gottingen–Heidelberg, 1963).Google Scholar
(5)Hochschild, G.The structure of Lie groups (Holden Day; San Francisco, 1965).Google Scholar
(6)Iwasawa, K.On some types of topological groups. Ann. of Math. (2) 50 (1949), 507–558.CrossRefGoogle Scholar
(7)Lee, D. H.On the homomorphisms of locally compact groups. Proc. Amer. Math. Soc. 37 (1973), 246–254.CrossRefGoogle Scholar
(8)Minbashian, F.Pro Affine Algebraic Groups. Amer. J. Math. 95 (1973), 174–192.CrossRefGoogle Scholar
(9)Montgomery, D. and Zippin, L.Topological transformation groups (Interscience; New York, 1955).Google Scholar
(10)Weil, A.L'integration dans les groupes topologiques et ses applications (Hermann; Paris, 1953).Google Scholar