Full paper in PDF:
$%A. G. Wasserman, Extending algebraic actions, Rev. Mat. Complut. 12 (1999), no. 2, 461–474.
%$
ABSTRACT
There is a well-known procedure —induction— for extending an action of a
subgroup of a Lie group
on a topological space
to an action of
on an associated space. Induction can also extend a smooth action of a
subgroup
of a Lie group
on a manifold
to a smooth action of
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
is a compact Abelian Lie group.
1991 Mathematics Subject Classification: 58A07, 14L30, 14P05.