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Transactions of the American Mathematical Society

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Reductivity and the automorphism group of locally compact groups


Author: Dong Hoon Lee
Journal: Trans. Amer. Math. Soc. 221 (1976), 379-389
MSC: Primary 22D45
DOI: https://doi.org/10.1090/S0002-9947-1976-0414782-7
MathSciNet review: 0414782
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Abstract: In this paper, we study reductivity of locally compact groups and its effect on the automorphism group and generalize the classical results on the automorphism group of analytic semisimple groups on the one hand and of compact groups on the other.


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  • [1] C. Chevalley, Théorie des groupes de Lie. Vol. 2: Groupes algébriques, Actualités Sci. Indust., no. 1152, Hermann, Paris, 1951. MR 14, 448. MR 0051242 (14:448d)
  • [2] H. Freudenthal, Ein Zerlegungssatz für im Kleinen kompakte Gruppen, Arch. Math. 15 (1964), 161-165. MR 29 #3571. MR 0166294 (29:3571)
  • [3] M. Gotô, Linear representations of topological groups, Proc. Amer. Math. Soc. 1 (1950), 425-437. MR 12, 479. MR 0038982 (12:479e)
  • [4] -, Dense embeddings of locally compact connected groups, Ann. of Math. (2) 61 (1955), 154-169. MR 16, 447. MR 0065567 (16:447b)
  • [5] S. Grosser, O. Loos and M. Moskowitz, Über Automorphismengruppen lokal-kompakter Gruppen und Derivationen von Lie-Gruppen, Math. Z. 114 (1970), 321-339. MR 41 #8575. MR 0263976 (41:8575)
  • [6] G. Hochschild and G. D. Mostow, Representations and representative functions of Lie groups, Ann. of Math. (2) 66 (1957), 495-542. MR 20 #5248. MR 0098796 (20:5248)
  • [7] K. Iwasawa, On some types of topological groups, Ann. of Math. (2) 50 (1949), 507-558. MR 10, 679. MR 0029911 (10:679a)
  • [8] D. H. Lee, Supplements for the identity component in locally compact groups, Math. Z. 104 (1968), 28-49. MR 36 #6534. MR 0223486 (36:6534)
  • [9] -, On deformations of homomorphisms of locally compact groups, Trans. Amer. Math. Soc. 191 (1974), 353-361. MR 0435284 (55:8244)
  • [10] M. Moskowitz, On pro-reductive groups, Proc. Cambridge Philos. Soc. 76 (1974), 401-406. MR 49 #10818. MR 0346092 (49:10818)
  • [11] G. D. Mostow, Cohomology of topological groups and solvmanifolds, Ann. of Math. (2) 73 (1961), 20-48. MR 23 #A2484. MR 0125179 (23:A2484)
  • [12] W. T. van Est, Dense embeddings of Lie groups, Nederl. Akad. Wetensch. Proc. Ser. A 54 = Indag. Math. 13 (1951), 321-328. MR 13, 432. MR 0044530 (13:432c)
  • [13] S. P. Wang, The automorphism group of a locally compact group, Duke Math. J. 36 (1969), 277-282. MR 39 #1589. MR 0240237 (39:1589)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0414782-7
Keywords: Reductivity, cochains, semisimple, conjugacy classes, orbits, radical, adjoint representation
Article copyright: © Copyright 1976 American Mathematical Society

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