| Groups which do not admit ghosts (2006) | |||||||||
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.. Comment: 9 pages, improved exposition and fixed several typos, to appear in the Proceedings of the AMS | |||||||||
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