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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
Citation: 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.
URI: http://hdl.handle.net/1942/3327
DOI: 10.1112/S0024611597000257
ISI #: A1997XJ78300002
ISSN: 0024-6115
Type: Journal Contribution
Appears in Collections: Research publications

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