Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

See all formats and pricing
More options …
Volume 2006, Issue 598


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


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.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Erik Friese and Frieder Ladisch
Journal of Algebraic Combinatorics, 2017

Comments (0)

Please log in or register to comment.
Log in