Publication
Title
Krull, Gelfand-Kirillov, Filter, Faithful and Schur dimensions
Author
Abstract
The aim of the paper is to explain relations between 5 mentioned dimensions. In Section 1 a connection is established between Krull, Gelfand-Kirillov and Filter dimension of simple affine algebras, and an analog of Bernstein's inequality is proved for nonzero finitely generated modules over simple affine algebras. These results are applied to compute the Krull dimension of the ring of differential operators on a smooth affine variety. In Section 2 the results of Section 1 are generalized for affine algebras (not necessarily simple). For a new dimension, the faithful dimension, is to be introduced. In Section 3 we consider the Schur dimension and its relations with holonomic modules over the ring of differential operators on a smooth affine variety. In particular, we prove that every holonomic module M which has multiplicity e(M) = 1 over the n'th Weyl algebra A(n) has Schur dimension sd(M) = 1. In Section 4 we give a review of (recent) results on the Krull dimension of skew Laurent extensions and generalized Weyl algebras with left Noetherian coefficients. This paper can be considered as an addition to and continuation of the paper of Tom Lenagan in the present volume.
Language
English
Source (journal)
Infinite length modules
Source (book)
Conference on Infinite Length Modules, SEP 07-11, 1998, BIELEFELD, GERMANY
Publication
2000
ISBN
3-7643-6413-0
Volume/pages
(2000), p. 149-166
ISI
000165048800007
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 03.01.2013
Last edited 01.10.2017
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