Some remarks on homeomorphisms of compact Lie groups
HTML articles powered by AMS MathViewer
- by S. C. Bagchi and A. Sitaram
- Proc. Amer. Math. Soc. 93 (1985), 159-163
- DOI: https://doi.org/10.1090/S0002-9939-1985-0766548-7
- PDF | Request permission
Abstract:
It is proved that if $G$ is a compact connected semisimple Lie group and $H$ a compact group of homeomorphisms of $G$ containing all left and right translations of $G$, then there exists a positive integer $k$ such that for any $\tau \in H$, ${\tau ^k}$ is, modulo a translation, an inner automorphism.References
- Z. Charzyński, Sur les transformations isométriques des espaces du type $(F)$, Studia Math. 13 (1953), 94–121 (French). MR 56193, DOI 10.4064/sm-13-1-94-121
- Irving Glicksberg, Some special transformation groups, Proc. Amer. Math. Soc. 11 (1960), 315–318. MR 116065, DOI 10.1090/S0002-9939-1960-0116065-5
- I. Glicksberg, Maps preserving translates of a function, Pacific J. Math. 87 (1980), no. 2, 323–334. MR 592739 —, Transition operator characterizations of compact and maximally almost periodic locally compact groups, preprint.
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
- L. S. Pontryagin, Topological groups, Gordon and Breach Science Publishers, Inc., New York-London-Paris, 1966. Translated from the second Russian edition by Arlen Brown. MR 0201557
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 159-163
- MSC: Primary 53C35; Secondary 22E46
- DOI: https://doi.org/10.1090/S0002-9939-1985-0766548-7
- MathSciNet review: 766548