Dense subgroups of Lie groups
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- by David Zerling PDF
- Proc. Amer. Math. Soc. 62 (1977), 349-352 Request permission
Abstract:
Let G be a dense analytic subgroup with compact center of an analytic group L. Then there exist closed vector subgroups W and U of G and a (CA) closed normal analytic subgroup M of G, which contains the center of G, such that $G = MWU,MW \cap U = M \cap W = \{e\}$, and WU is a closed vector subgroup of G. Moreover, $L = MW\bar U$, where MW is a closed normal analytic subgroup of L and $\bar U$ is a toral group, such that $MW \cap \bar U$ is finite.References
- Morikuni Goto, Analytic subgroups of $\textrm {GL}(n,\,\textbf {R})$, Tohoku Math. J. (2) 25 (1973), 197β199. MR 322099, DOI 10.2748/tmj/1178241378
- W. T. van Est, Dense imbeddings of Lie groups, Nederl. Akad. Wetensch. Proc. Ser. A. 54 = Indagationes Math. 13 (1951), 321β328. MR 0044530
- David Zerling, Some theorems on $(\textrm {CA})$ analytic groups, Trans. Amer. Math. Soc. 205 (1975), 181β192. MR 364548, DOI 10.1090/S0002-9947-1975-0364548-0 β, Some theorems on (CA) analytic groups. II, TΓ΄hoku Math. J. (to appear).
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 349-352
- MSC: Primary 22E20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0435289-3
- MathSciNet review: 0435289