Groups which do not admit ghosts
Representation Theory
2009-12-03 v2 Group Theory
Abstract
A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module categories have no non-trivial ghosts are the cyclic groups of order 2 and 3. We compare this to the situation in the derived category of a commutative ring. We also determine for which groups G the second power of the Jacobson radical of kG is stably isomorphic to a suspension of k.
Cite
@article{arxiv.math/0610423,
title = {Groups which do not admit ghosts},
author = {Sunil K. Chebolu and J. Daniel Christensen and Jan Minac},
journal= {arXiv preprint arXiv:math/0610423},
year = {2009}
}
Comments
9 pages, improved exposition and fixed several typos, to appear in the Proceedings of the AMS