The Global Dimension of Rings of Differential Operators on Projective Spaces | Zendy

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The Global Dimension of Rings of Differential Operators on Projective Spaces

Author(s) -

Shelton Brad

Publication year - 1992

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/24.2.148

Subject(s) - mathematics , global dimension , dimension (graph theory) , embedding , pure mathematics , projective space , complex dimension , infinity , differential (mechanical device) , projective test , space (punctuation) , dimension theory (algebra) , complex projective space , algebra over a field , mathematical analysis , linguistics , philosophy , artificial intelligence , computer science , engineering , aerospace engineering

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

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