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Groups which do not admit ghosts
Author(s):
Sunil
K.
Chebolu;
J.
Daniel
Christensen;
Ján
Minác
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1171-1179.
MSC (2000):
Primary 20C20, 20J06;
Secondary 55P42
Posted:
December 6, 2007
Corrigenda:
Proc. Amer. Math. Soc. 136 (2008), 3727
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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  .
References:
-
- 1.
- D. J. Benson.
Representations and cohomology. I, volume 30 of Cambridge Studies in Advanced Mathematics.
Cambridge University Press, Cambridge, 1998. MR 1644252 (99f:20001a) - 2.
- D. J. Benson and Jon F. Carlson.
Products in negative cohomology.
J. Pure Appl. Algebra, 82(2):107-129, 1992. MR 1182934 (93i:20058) - 3.
- David Benson, Sunil K. Chebolu, J. Daniel Christensen, and Ján Mináč.
The generating hypothesis for the stable module category of a  -group.
Journal of Algebra, 310(1):428-433, 2007. MR 2307802 (2007k:16011) - 4.
- Jon F. Carlson.
Modules and group algebras.
Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1996.
Notes by Ruedi Suter. MR 1393196 (97c:20013) - 5.
- J. Daniel Christensen.
Ideals in triangulated categories: phantoms, ghosts and skeleta.
Adv. in Math., 136:284-339, 1998. MR 1626856 (99g:18007) - 6.
- Peter Freyd.
Stable homotopy.
In Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965), pages 121-172. Springer, New York, 1966. MR 0211399 (35:2280) - 7.
- S. A. Jennings.
The structure of the group ring of a  -group over a modular field.
Trans. Amer. Math. Soc., 50:175-185, 1941. MR 0004626 (3:34f) - 8.
- Keir Lockridge.
The generating hypothesis in the derived category of  -modules.
Journal of Pure and Applied Algebra, 208(2):485-495, 2007. MR 2277690 - 9.
- D. W. Sharpe and P. Vámos.
Injective modules.
Cambridge University Press, London, 1972. MR 0360706 (50:13153) - 10.
- Charles A. Weibel.
An introduction to homological algebra, volume 38 of Cambridge Studies in Advanced Mathematics.
Cambridge University Press, Cambridge, 1994. MR 1269324 (95f:18001)
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Additional Information:
Sunil
K.
Chebolu
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, Canada
Email:
schebolu@uwo.ca
J.
Daniel
Christensen
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, Canada
Email:
jdc@uwo.ca
Ján
Minác
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, Canada
Email:
minac@uwo.ca
DOI:
10.1090/S0002-9939-07-09058-2
PII:
S 0002-9939(07)09058-2
Keywords:
Ghost map,
stable module category,
derived category,
Jennings' theorem,
generating hypothesis.
Received by editor(s):
October 13, 2006,
Received by editor(s) in revised form:
January 2, 2007
Posted:
December 6, 2007
Communicated by:
Paul Goerss
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