Semialgebraic groups and the local closure of an orbit in a homogeneous space
Author:
Morikuni Goto
Journal:
Trans. Amer. Math. Soc. 247 (1979), 301315
MSC:
Primary 57S20; Secondary 22D05
MathSciNet review:
517696
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Abstract: Let L be a topological group acting on a locally compact Hausdorff space M as a transformation group. Let m be in M. A subset Q of M is called the local closure of the orbit Lm if Q is the smallest locally compact invariant subset of M with . A partition is called an LCpartition of M with respect to the L action if each is the local closure of Lm for any m in . Theorem. Let G be a connected Lie group, and let A and B be subgroups of G with only finitely many connected components. Suppose that B is closed. Then the factor space has an LCpartition with respect to the A action.
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 M. Goto, Orbits of oneparameter groups. III. Lie group case, J. Math. Soc. Japan 23 (1971), 95102. MR 0279238 (43:4961)
 [2]
 , Products of two semialgebraic groups, J. Math. Soc. Japan 25 (1973), 7174. MR 0315050 (47:3599)
 [3]
 M. Goto and H. C. Wang, Nondiscrete uniform subgroups of semisimple Lie groups, Math. Ann. 198 (1972), 259286. MR 0354934 (50:7411)
 [4]
 S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
 [5]
 K. Iwasawa, On some types of topological groups, Ann. of Math. 50 (1949), 507558. MR 0029911 (10:679a)
 [6]
 L. Pukanszky, Unitary representations of solvable Lie groups, Ann. Sci. École Norm. Sup. 4 (1971), 457608. MR 0439985 (55:12866)
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DOI:
http://dx.doi.org/10.1090/S0002994719790517696X
PII:
S 00029947(1979)0517696X
Article copyright:
© Copyright 1979
American Mathematical Society
