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Abstract
For a finite group G acting faithfully on euclidean space we consider the convex hull of the orbit of a suitable vector. We show that the combinatorial structure of this polytope determines a polynomial growth free ℤG-resolution of ℤ. A resolution due to De Concini and Salvetti is recovered when G is a finite reflection group. A resolution based on the simplex is obtained from the regular representation of a finite group. □
Our aim in this paper is to explain how, for any finite group G, a finite calculation involving convex hulls leads to an explicit recursive description of all dimensions of a free ℤG-resolution in which the number of generators grows polynomially with dimension.
Received: 2004-08-19
Revised: 2005-06-29
Published Online: 2006-11-26
Published in Print: 2006-09-01
© Walter de Gruyter
