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$%A. G. Wasserman, Extending algebraic actions, Rev. Mat. Complut. 12 (1999), no. 2, 461–474.
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Extending Algebraic Actions
Arthur G. WASSERMAN
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109-1109 — USA
Received: February 17, 1999
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.