1999
DOI: 10.1017/s0305004198002965
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d-Simple rings and simple -modules

Abstract: We use certain derivations of a polynomial ring, that do not leave any proper non-zero ideal invariant, to construct simple non-holonomic modules over the nth Weyl algebra. This approach extends to the rings of differential operators of other smooth affine varieties, like smooth quadric surfaces.

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Cited by 19 publications
(14 citation statements)
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“…, r + s), the polynomial P (a,b j ) (X) (respectively P (−a,b j ) (X)) can be computed. Then, of course, one can effectively determine whether the properties (ii)(0)- (2) are satisfied.…”
Section: Theorem B (The Algorithm In the ''Local'' Case) Let Rmentioning
confidence: 99%
“…, r + s), the polynomial P (a,b j ) (X) (respectively P (−a,b j ) (X)) can be computed. Then, of course, one can effectively determine whether the properties (ii)(0)- (2) are satisfied.…”
Section: Theorem B (The Algorithm In the ''Local'' Case) Let Rmentioning
confidence: 99%
“…, x n ] are not easy to find. A family of linear simple derivations was discovered by Coutinho in [3] (generalizing an example of Stafford) and is based on a result of Shamsuddin (see [10]). Families of simple quadratic derivations of K[x 1 , x 2 ] were found by Maciejewski, Moulin-Ollagnier and Nowicki in [9].…”
Section: Proof It Is Enough To Show That (Ii) ⇒ (I) Suppose Thatmentioning
confidence: 99%
“…Stafford's examples were generalized by Coutinho in [3]. Another objective also treated in section 3 is to generalize to K[x 1 , .…”
Section: Introduction Letmentioning
confidence: 99%
“…More recently, the d-simplicity of the ring of polynomials has also been used to produce new examples of nonholonomic irreducible modules over the Weyl algebra; see [4,7].…”
Section: Introductionmentioning
confidence: 99%