Rings of differential operators on invariant rings of tori

Differential operators on monomial rings

Rings of differential operators are notoriously difficult to compute. This paper computes the ring of differential operators on a Stanley-Reisner ring R. The D-module structure of R is determined. This yields a new proof that Nakai’s conjecture holds for Stanley-Reisner rings. An application to tight closure is described. @ 1999 Elsevier Science B.V. All rights reserved. AMS Clas.@cation: Prima...

Differential Polynomial Rings of Triangular Matrix Rings

Explicit Calculations in Rings of Differential Operators

— We use the notion of a standard basis to study algebras of linear differential operators and finite type modules over these algebras. We consider the polynomial and the holomorphic cases as well as the formal case. Our aim is to demonstrate how to calculate classical invariants of germs of coherent (left) modules over the sheaf D of linear differential operators over Cn. The main invariants w...

Graded cofinite rings of differential operators

In this paper we study subalgebras A of the algebra D(X) of differential operators on a smooth variety X which are big in the following sense: using the order of a differential operator, the ring D(X) is equipped with a filtration. Its associated graded algebra D(X) is commutative and can be regarded as the set of regular functions on the cotangent bundle ofX . The subalgebra A inherits a filtr...

Mad Subalgebras of Rings of Differential Operators on Curves

We study the maximal abelian ad-nilpotent (mad) subalgebras of the domains D Morita equivalent to the first Weyl algebra. We give a complete description both of the individual mad subalgebras and of the space of all such. A surprising consequence is that this last space is independent of D . Our results generalize some classic theorems of Dixmier about the Weyl algebra.