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Algebras with finitely generated invariant subalgebras. (English) Zbl 1099.13500
Summary: We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.

MSC:
13A50 Actions of groups on commutative rings; invariant theory
13E15 Commutative rings and modules of finite generation or presentation; number of generators
14L17 Affine algebraic groups, hyperalgebra constructions
14L30 Group actions on varieties or schemes (quotients)
14M17 Homogeneous spaces and generalizations
14R20 Group actions on affine varieties
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