Embeddings of differential operator rings and Goldie dimension

Author:
Declan Quinn

Journal:
Proc. Amer. Math. Soc. **102** (1988), 9-16

MSC:
Primary 16A05,; Secondary 17B30,17B35

DOI:
https://doi.org/10.1090/S0002-9939-1988-0915706-X

MathSciNet review:
915706

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Abstract: The differential operator ring can be embedded in , the first Weyl algebra over , where is a -algebra and is a locally nilpotent derivation on . Furthermore is again a differential operator ring over the image of . We consider similar embeddings of the smash product , where is a finite dimensional Lie algebra and is its universal enveloping algebra. We show that the Weyl algebra over has the same Goldie dimension as itself and use this to prove that and have the same Goldie dimension where is again a -algebra and is locally nilpotent.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0915706-X

Article copyright:
© Copyright 1988
American Mathematical Society