The generating hypothesis for the stable module category of a $p$-group
Representation Theory
2009-12-03 v3 Algebraic Topology
Abstract
Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's generating hypothesis holds for a non-trivial finite p-group G if and only if G is either C_2 or C_3. We also give various conditions which are equivalent to the generating hypothesis.
Keywords
Cite
@article{arxiv.math/0611403,
title = {The generating hypothesis for the stable module category of a $p$-group},
author = {David J. Benson and Sunil K. Chebolu and J. Daniel Christensen and Jan Minac},
journal= {arXiv preprint arXiv:math/0611403},
year = {2009}
}
Comments
6 pages, fixed minor typos, to appear in J. Algebra