Groups which do not admit ghosts
Authors:
Sunil K. Chebolu, J. Daniel Christensen and Ján Minác
Journal:
Proc. Amer. Math. Soc. 136 (2008), 1171-1179
MSC (2000):
Primary 20C20, 20J06; Secondary 55P42
DOI:
https://doi.org/10.1090/S0002-9939-07-09058-2
Published electronically:
December 6, 2007
Corrigendum:
Proc. Amer. Math. Soc. 136 (2008), 3727
MathSciNet review:
2367091
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 
.
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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:
https://doi.org/10.1090/S0002-9939-07-09058-2
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
Published electronically:
December 6, 2007
Communicated by:
Paul Goerss
