Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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 $ 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 $ C_2$ and $ C_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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20C20, 20J06, 55P42

Retrieve articles in all journals with MSC (2000): 20C20, 20J06, 55P42


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: http://dx.doi.org/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
Published electronically: December 6, 2007
Communicated by: Paul Goerss