There is a well-known procedure -induction- for extending an action of a subgroup H of a Lie group G on a topological space X to an action of G on an associated space. Induction can also extend a smooth action of a subgroup H of a Lie group G on a manifold M to a smooth action of G on an associated manifold. In this paper elementary methods are used to show that induction also works in the category of (nonsingular) real algebraic varieties and regular or entire maps if G is a compact abelian Lie group.
@article{urn:eudml:doc:44405,
title = {Extending algebraic actions.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {12},
year = {1999},
pages = {463-474},
zbl = {0963.58001},
mrnumber = {MR1740470},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44405}
}
Wasserman, Arthur G. Extending algebraic actions.. Revista Matemática de la Universidad Complutense de Madrid, Tome 12 (1999) pp. 463-474. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44405/