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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

Online
ISSN
1435-5345
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Volume 2006, Issue 598

Issues

Polytopal resolutions for finite groups

Graham Ellis / James Harris / Emil Sköldberg
Published Online: 2006-11-26 | DOI: https://doi.org/10.1515/CRELLE.2006.071

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.

About the article

Received: 2004-08-19

Revised: 2005-06-29

Published Online: 2006-11-26

Published in Print: 2006-09-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2006, Issue 598, Pages 131–137, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2006.071.

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