Automorphism groups of locally compact reductive groups
HTML articles powered by AMS MathViewer
- by T. S. Wu PDF
- Proc. Amer. Math. Soc. 106 (1989), 537-542 Request permission
Abstract:
A topological group $G$ is reductive if every continuous finite dimensional $G$-module is semi-simple. We study the structure of those locally compact reductive groups which are the extension of their identity components by compact groups. We then study the automorphism groups of such groups in connection with the groups of inner automorphisms. Proposition. Let $G$ be a locally compact reductive group such that $G/{G_0}$ is compact. Then $I\left ( {{G_0}} \right )$ is dense in ${A_0}\left ( G \right )$.References
- Patrick B. Chen and Ta Sun Wu, On the automorphism groups of locally compact groups and on a theorem of M. Goto, Tamkang J. Math. 17 (1986), no. 2, 99–116. MR 872682
- Morikuni Gotô, Linear representations of topological groups, Proc. Amer. Math. Soc. 1 (1950), 425–437. MR 38982, DOI 10.1090/S0002-9939-1950-0038982-0
- Siegfried Grosser, Ottmar Loos, and Martin Moskowitz, Über Automorphismengruppen lokal-kompakter Gruppen und Derivationen von Lie-Gruppen, Math. Z. 114 (1970), 321–339 (German). MR 263976, DOI 10.1007/BF01110384
- G. Hochschild, The structure of Lie groups, Holden-Day, Inc., San Francisco-London-Amsterdam, 1965. MR 0207883
- Kenkichi Iwasawa, On some types of topological groups, Ann. of Math. (2) 50 (1949), 507–558. MR 29911, DOI 10.2307/1969548
- Dong Hoon Lee, Supplements for the identity component in locally compact groups, Math. Z. 104 (1968), 28–49. MR 223486, DOI 10.1007/BF01114916
- Dong Hoon Lee, Reductivity and the automorphism group of locally compact groups, Trans. Amer. Math. Soc. 221 (1976), no. 2, 379–389. MR 414782, DOI 10.1090/S0002-9947-1976-0414782-7
- G. Hochschild and G. D. Mostow, Representations and representative functions of Lie groups, Ann. of Math. (2) 66 (1957), 495–542. MR 98796, DOI 10.2307/1969906
- G. D. Mostow, Cohomology of topological groups and solvmanifolds, Ann. of Math. (2) 73 (1961), 20–48. MR 125179, DOI 10.2307/1970281
- G. D. Mostow, Arithmetic subgroups of groups with radical, Ann. of Math. (2) 93 (1971), 409–438. MR 289713, DOI 10.2307/1970882
- Howard Garland and Morikuni Goto, Lattices and the adjoint group of a Lie group, Trans. Amer. Math. Soc. 124 (1966), 450–460. MR 199311, DOI 10.1090/S0002-9947-1966-0199311-1
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 537-542
- MSC: Primary 22D05; Secondary 22E15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0968626-X
- MathSciNet review: 968626