Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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 $ m\, \in \,Q$. A partition

$\displaystyle M = \,\bigcup\limits_{\lambda \in \wedge } \,{Q_\lambda },\,\,\,\... ...,}}\, \cap \,\,{Q_\mu } = \,\emptyset \,\,\,\,\left( {\lambda \ne \mu } \right)$

is called an LC-partition of M with respect to the L action if each $ {Q_\lambda }$ is the local closure of Lm for any m in $ {Q_\lambda }$.

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 $ G/B$ has an LC-partition with respect to the A action.


References [Enhancements On Off] (What's this?)


Similar Articles

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: http://dx.doi.org/10.1090/S0002-9947-1979-0517696-X
PII: S 0002-9947(1979)0517696-X
Article copyright: © Copyright 1979 American Mathematical Society