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Groups which do not admit ghosts |
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| Authors: | Sunil K. Chebolu J. Daniel Christensen Já n Miná c |
| Affiliation: | Department of Mathematics, University of Western Ontario, London, Ontario, Canada ; Department of Mathematics, University of Western Ontario, London, Ontario, Canada ; Department of Mathematics, University of Western Ontario, London, Ontario, Canada |
| Abstract: | A ghost in the stable module category of a group  is a map between representations of  that is invisible to Tate cohomology. We show that the only non-trivial finite  -groups whose stable module categories have no non-trivial ghosts are the cyclic groups  and  . We compare this to the situation in the derived category of a commutative ring. We also determine for which groups  the second power of the Jacobson radical of  is stably isomorphic to a suspension of  . |
| Keywords: | Ghost map stable module category derived category Jennings' theorem generating hypothesis. |
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