Differential dimension polynomials of finitely generated extensions

Standard Bases in Finitely Generated Difference-Skew-Differential Modules and Their Application to Dimension Polynomials

This thesis treats different kinds of standard bases in finitely generated modules over the ring of difference-skew-differential operators, their computation and their application to the computation of multivariate dimension (quasi-)polynomials. It consists of two parts. The first deals with standard bases in modules over the ring of difference-skew-differential operators. The second part deals...

Multivariable Dimension Polynomials and New Invariants of Differential Field Extensions

We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin’s theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension. 2000 Mathematics Subject Classification. 12H05, 12H20, 13N15.

Representation Dimension and Finitely Generated Cohomology

We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal complexity occurring among its modules. This provides a unified approach to computing lower bounds for the representation dimension of group algebras, exterior alge...

Computation of Bivariate Dimension Polynomials of Finitely Generated D-Modules Using Maple

In this paper we present an implementation for computing bivariate dimension polynomials of finitely generated modules over a Weyl algebra in Maple. We recall some basic results in order to explain the notion of dimension polynomials and to introduce methods for their computation based on Gröbner basis techniques. We explain input options for the mentioned implementations and provide several ex...

The Kolchin Seminar in Differential Algebra Finitely Generated Difference Field Extensions