Semi-algebraic groups and the local closure of an orbit in a homogeneous space

Author:
Morikuni Goto

Journal:
Trans. Amer. Math. Soc. **247** (1979), 301-315

MSC:
Primary 57S20; Secondary 22D05

DOI:
https://doi.org/10.1090/S0002-9947-1979-0517696-X

MathSciNet review:
517696

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

*partition*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 LC-partition with respect to the A action.*

**[1]**M. Goto,*Orbits of one-parameter groups*. III.*Lie group case*, J. Math. Soc. Japan**23**(1971), 95-102. MR**0279238 (43:4961)****[2]**-,*Products of two semi-algebraic groups*, J. Math. Soc. Japan**25**(1973), 71-74. MR**0315050 (47:3599)****[3]**M. Goto and H. C. Wang,*Non-discrete uniform subgroups of semisimple Lie groups*, Math. Ann.**198**(1972), 259-286. 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), 507-558. MR**0029911 (10:679a)****[6]**L. Pukanszky,*Unitary representations of solvable Lie groups*, Ann. Sci. École Norm. Sup.**4**(1971), 457-608. MR**0439985 (55:12866)**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
57S20,
22D05

Retrieve articles in all journals with MSC: 57S20, 22D05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0517696-X

Article copyright:
© Copyright 1979
American Mathematical Society