Morita invariance of the filter dimension and of the inequality of Bernstein

Details Morita invariance of the filter dimension and of the inequality of Bernstein Morita invariance of the filter dimension and of the inequality of Bernstein

2006-10-29

arxiv.org/abs/math/0610900v1

Mathematics

Rings and Algebras

8 pages

Scientific paper

It is proved that the filter dimenion is Morita invariant. A direct consequence of this fact is the Morita invariance of the inequality of Bernstein: if an algebra $A$ is Morita equivalent to the ring $\CD (X)$ of differential operators on a smooth irreducible affine algebraic variety $X$ of dimension $n\geq 1$ over a field of characteristic zero then the Gelfand-Kirillov dimension $ \GK (M)\geq n = \frac{\GK (A)}{2}$ for all nonzero finitely generated $A$-modules $M$. In fact, a more strong result is proved, namely, a Morita invariance of the holonomic number for finitely generated algebra. As a direct consequence of this fact an affirmative answer is given to the question/conjecture posed by Ken Brown several years ago of whether an analogue of the inequality of Bernstein holds for the (simple) rational Cherednik algebras $H_c$ for integral $c$: $\GK (M)\geq n =\frac{\GK (H_c)}{2}$ for all nonzero finitely generated $H_c$-modules $M$.

Affiliated with

Also associated with

No associations

Rating

Morita invariance of the filter dimension and of the inequality of Bernstein does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Morita invariance of the filter dimension and of the inequality of Bernstein, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Morita invariance of the filter dimension and of the inequality of Bernstein will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-652119