Can the Weyl algebra be a fixed ring?

Smith, S. P.

doi:10.1090/S0002-9939-1989-0962247-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Can the Weyl algebra be a fixed ring?
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by S. P. Smith PDF

Proc. Amer. Math. Soc. 107 (1989), 587-589 Request permission

Abstract:

If a finite soluble group acts as automorphisms of a domain, then the invariant subring is not isomorphic to the first Weyl algebra ${\mathbf {C}}[t,d/dt]$.

References

Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Fasc. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). MR 0498737

Overrings of primitive factor rings of

J. T. Stafford, Endomorphisms of right ideals of the Weyl algebra, Trans. Amer. Math. Soc. 299 (1987), no. 2, 623–639. MR 869225, DOI 10.1090/S0002-9947-1987-0869225-3