Orbits of Distal Actions on Locally Compact Groups
Journal of Lie Theory, Tome 22 (2012) no. 2, pp. 587-599
Voir la notice de l'article provenant de la source Heldermann Verlag
We discuss properties of orbits of (semi)group actions on locally compact groups G. In particular, we show that if a compactly generated locally compact abelian group acts distally on G then the closure of each of its orbits is a minimal closed invariant set (i.e. the action has [MOC]). We also show that for such an action distality is preserved if we go modulo any closed normal invariant subgroup and hence [MOC] is also preserved. We also show that any semigroup action on G has [MOC] if and only if the corresponding actions on a compact invariant metrizable subgroup K and on the quotient space G/K have [MOC].
Classification :
37B05, 22D05, 22D45
Mots-clés : Distal group actions, Minimal orbit closures, Generalised FC-groups
Mots-clés : Distal group actions, Minimal orbit closures, Generalised FC-groups
Affiliations des auteurs :
Riddhi Shah 1
Riddhi Shah. Orbits of Distal Actions on Locally Compact Groups. Journal of Lie Theory, Tome 22 (2012) no. 2, pp. 587-599. http://geodesic.mathdoc.fr/item/JOLT_2012_22_2_a12/
@article{JOLT_2012_22_2_a12,
author = {Riddhi Shah},
title = {Orbits of {Distal} {Actions} on {Locally} {Compact} {Groups}},
journal = {Journal of Lie Theory},
pages = {587--599},
year = {2012},
volume = {22},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_2_a12/}
}