Sunil K. Chebolu, J. Daniel Christensen, Jan Minac
Published 2006-10-12, updated 2007-01-05Version 2
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.
Comments: 9 pages, improved exposition and fixed several typos, to appear in the Proceedings of the AMS
Journal: Proc. Amer. Math. Soc. 136 (2008) 1171-1179
The generating hypothesis for the stable module category of a $p$-group
Separable commutative rings in the stable module category of cyclic groups
Freyd's generating hypothesis with almost split sequences
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