This is the homepage of the FWF-Project P16641
Relation Modules for Conjugate Algebraic Numbers
at the Institute of Mathematics of the University of Innsbruck.
The aim of the Project is to develop a better understanding of the mathematical structures associated with the algebraic relations between the zeros of a univariate, separable polynomial f with coefficients in an arbitrary field K. Clearly the most important case emerges if we choose f to be irreducible and K to be the rational numbers. If x is the vector of all zeros of f in the algebraic closure of K, then a polynomial vanishing at x is called a relation. All relations form the relation ideal of f. It is in the center of our considerations. Of special interest are also the so-called linear relations. These are relations of degree one, i.e. they express K-linear dependence of the zeros of f . For the investigation of these special relations representation theory proved to be a very powerful tool. Other methods and theories used are Galois theory , algebraic geometry, Gr�bner bases and invariant theory .
The project started in October 2003. Besides the non-stop engagement of the two associate Professors Kurt Girstmair and Franz Pauer, Mathias Lederer with his diploma thesis and his PhD thesis, made significant contributions in the beginning. He now holds an assistant position at the University of Bielefeld. For his present activities see here. In December 2004 Michael Wibmer got involved in the project. He has finished his diploma thesis and is working on PhD level now.
Michael Wibmer, Gr�bner Bases for Families of Affine or Projective Schemes, preprint, 2006, pdf
Mathias Lederer, The vanishing ideal of a finite set of closed points in affine space, preprint, 2006, pdf
Kurt Girstmair, The Galois Relation x1=x2+x3 and Fermat over Finite Fields, to appear in Acta Arithmetica, 2006, pdf
Mathias Lederer, A determinant-like formula for the Kostka numbers, to appear in Annals of Combinatorics, 2005, pdf
Kurt Girstmair, Franz Pauer, Michael Wibmer, On invariant relations between zeros of polynomials, Communications in Algebra, Volume 33, Number 7, 2157-2166, 2005
Michael Wibmer , Invariante Relationen zwischen konjugierten algebraischen Zahlen, Diplomarbeit, 2005, pdf
Mathias Lederer, Relation ideals and the Buchberger-M�ller Algorithm, preprint, 2005, pdf
Mathias Lederer, Relationenmoduln f�r konjugierte algebraische Zahlen, Dissertation, 2004, pdf
Mathias Lederer, Explizite Konstruktionen in Zerf�llungsk�rpern von Polynomen, Diplomarbeit, 2002, pdf
|last modified on 5/11/2007 15:20:32 by Michael Wibmer|