Full paper in PDF:
$%A. G. Wasserman, Extending algebraic actions, Rev. Mat. Complut. 12 (1999), no. 2, 461–474.
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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.