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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.
Wasserman, Arthur G.. "Extending algebraic actions.." Revista Matemática Complutense 12.2 (1999): 463-474. <http://eudml.org/doc/44405>.
@article{Wasserman1999, abstract = {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.}, author = {Wasserman, Arthur G.}, journal = {Revista Matemática Complutense}, keywords = {Espacio topológico; Algebras; Variedad algebraica; Lie group; topological space; real algebraic varieties}, language = {eng}, number = {2}, pages = {463-474}, title = {Extending algebraic actions.}, url = {http://eudml.org/doc/44405}, volume = {12}, year = {1999}, }
TY - JOUR AU - Wasserman, Arthur G. TI - Extending algebraic actions. JO - Revista Matemática Complutense PY - 1999 VL - 12 IS - 2 SP - 463 EP - 474 AB - 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. LA - eng KW - Espacio topológico; Algebras; Variedad algebraica; Lie group; topological space; real algebraic varieties UR - http://eudml.org/doc/44405 ER -