Groups which do not admit ghosts

Details Groups which do not admit ghosts Groups which do not admit ghosts

2006-10-12

arxiv.org/abs/math/0610423v2

Proc. Amer. Math. Soc. 136 (2008) 1171-1179

Mathematics

Representation Theory

9 pages, improved exposition and fixed several typos, to appear in the Proceedings of the AMS

Scientific paper

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.

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