Freyd's generating hypothesis with almost split sequences
Representation Theory
2009-12-03 v2 Algebraic Topology
Abstract
Freyd's generating hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's generating hypothesis fails for kG when the Sylow p-subgroup of G has order at least 4 using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's generating hypothesis for the stable module category of a finite group. We also derive some consequences of the generating hypothesis.
Keywords
Cite
@article{arxiv.0806.2165,
title = {Freyd's generating hypothesis with almost split sequences},
author = {Jon F. Carlson and Sunil K. Chebolu and Jan Minac},
journal= {arXiv preprint arXiv:0806.2165},
year = {2009}
}
Comments
6 pages, fixed minor typos, final version, to appear in Proc. Amer. Math. Soc