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A Bernstein-Gabber-Joseph theorem for affine algebras*

Published online by Cambridge University Press:  20 January 2009

V. V. Bavula  and
T. H. Lenagan
V. V. Bavula
Affiliation:
Department of Mathematics, Kiev University, Vladimirskaya Str, 64 Kiev 252617Ukraine E-mail address: [email protected]
T. H. Lenagan
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building King's Buildings Mayfield Road, EdinburghEH9 3JZ E-mail address: [email protected]
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Bernstein's famous result, that any non-zero module M over the n-th Weyl algebra An satisfies GKdim(M)≥GKdim(An)/2, does not carry over to arbitrary simple affine algebras, as is shown by an example of McConnell. Bavula introduced the notion of filter dimension of simple algebra to explain this failure. Here, we introduce the faithful dimension of a module, a variant of the filter dimension, to investigate this phenomenon further and to study a revised definition of holonomic modules. We compute the faithful dimension for certain modules over a variant of the McConnell example to illustrate the utility of this new dimension.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 311 - 332
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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