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The Global Dimension of Rings of Differential Operators on Projective Spaces

The Global Dimension of Rings of Differential Operators on Projective Spaces We compute the global dimension of the twisted rings of global differential operators Dλ on complex projective n‐space. As λ varies through the complex numbers, this global dimension takes on the values n, 2n and infinity. We also study the embedding of Dλ in the Weyl algebra An in the cases when the global dimension is infinite. In these cases, we see that the flat dimension of An as a Dλ‐module is infinite as well. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

The Global Dimension of Rings of Differential Operators on Projective Spaces

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/24.2.148
Publisher site
See Article on Publisher Site

Abstract

We compute the global dimension of the twisted rings of global differential operators Dλ on complex projective n‐space. As λ varies through the complex numbers, this global dimension takes on the values n, 2n and infinity. We also study the embedding of Dλ in the Weyl algebra An in the cases when the global dimension is infinite. In these cases, we see that the flat dimension of An as a Dλ‐module is infinite as well.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Mar 1, 1992

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