Computational Koszul Homology and Spencer Cohomology - Research Information System | University of Kassel

without external funding

Computational Koszul Homology and Spencer Cohomology

Project Details

Project duration: 10/2006–10/2010

Abstract

The project studies effective methods for the explicit determination of the Koszul homology of polynomial modules (or dually the Spencer cohomology of comodules). This is in principle equivalent to the computation of a minimal free resolution, however, it is still an open problem to find an explicit representation of the required isomorphism. We study various direct methods for the construction of the Koszul homology first of monomial modules and then of polynomial modules. In the monomial case we use different techniques of combinatorial, topological or algebraic origin. One possibility for an extension to the polynomial case is via homological perturbation theory. We are also interested in the precise relationship between Pommaret bases and the Koszul homology (or Spencer cohomology, resp.).

Research Areas

Mathematics

Publications

2010	Seiler, W., 2010. Involution - The Formal Theory of Differential Equations and its Applications in Computer Algebra. Springer-Verlag, Berlin/Heidelberg.
2008	Saenz de Cabezon, E., 2008. Computational Koszul Homology: Computations and Applications. Universidad de La Rioja, Logrono.
2007	Seiler, W., 2007. Spencer Cohomology, Differential Equations, and Pommaret Bases, in: M. Rosenkranz, D.M.W. (Hrsg.), Gröbner Bases and Symbolic Analysis. de Gruyter, Berlin, S. 169–216. https://doi.org/10.1515/9783110922752.169
2006	Hausdorf, M., Sahbi, M., Seiler, W., 2006. Delta- and Quasi-Regularity for Polynomial Ideals, in: Seiler, W.M. (Hrsg.), Global Integrability of Field Theorie - GIFT 2006. Universitätsverlag Karlsruhe, Karlsruhe, S. 179–200.