Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/3327
Title: | Simplicity of rings of differential operators in prime characteristic | Authors: | Smith, KE VAN DEN BERGH, Michel |
Issue Date: | 1997 | Publisher: | LONDON MATH SOC | Source: | PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 75(1). p. 32-62 | Abstract: | Let $W$ be a finite dimensional representation of a linearly reductive group $G$ over a field $k$. Motivated by their work on classical rings of invariants, Levasseur and Stafford asked whether the ring of invariants under $G$ of the symmetric algebra of $W$ has a simple ring of differential operators. In this paper, we show that this is true in prime characteristic. Indeed, if $R$ is a graded subring of a polynomial ring over a perfect field of characteristic $p>0$ and if the inclusion $R\hookrightarrow S$ splits, then $D_k(R)$ is a simple ring. In the last section of the paper, we discuss how one might try to deduce the characteristic zero case from this result. As yet, however, this is a subtle problem and the answer to the question of Levasseur and Stafford remains open in characteristic zero. | Notes: | LIMBURGS UNIV CTR,DEPT WNI,B-3590 DIEPENBEEK,BELGIUM.Smith, KE, MIT,77 MASSACHUSETTS AVE,CAMBRIDGE,MA 02139. | Document URI: | http://hdl.handle.net/1942/3327 | DOI: | 10.1112/S0024611597000257 | ISI #: | A1997XJ78300002 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
0209275v1.pdf | 339.58 kB | Adobe PDF | View/Open |
SCOPUSTM
Citations
62
checked on Sep 3, 2020
WEB OF SCIENCETM
Citations
85
checked on Apr 22, 2024
Page view(s)
72
checked on Nov 7, 2023
Download(s)
114
checked on Nov 7, 2023
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.