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Simplicity of Rings of Differential Operators in Prime Characteristic | | Karen E. Smith
; Michel Van den Bergh
; | | Date: |
20 Sep 2002 | | Journal: | Proc. London Math. Soc. (3) 75 (1997), no. 1, 32--62 | | Subject: | Representation Theory; Rings and Algebras; Commutative Algebra MSC-class: 16S32; 16G60, 13A35 | math.RT math.AC math.RA | | 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 inclusionof R into 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. | | Source: | arXiv, math.RT/0209275 | | Services: | Forum | Review | PDF | Favorites | |
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