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Freyd's generating hypothesis with almost split sequences
Author(s):
Jon
F.
Carlson;
Sunil
K.
Chebolu;
Ján
Minác
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2575-2580.
MSC (2000):
Primary 20C20, 20J06;
Secondary 55P42
Posted:
February 6, 2009
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Abstract:
Freyd's generating hypothesis for the stable module category of a non-trivial finite group  is the statement that a map between finitely generated  -modules that belongs to the thick subcategory generated by the field  factors through a projective module if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's generating hypothesis fails for  when the Sylow  -subgroup of  has order at least  using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's generating hypothesis for the stable module category of a finite group. We also derive some consequences of the generating hypothesis.
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Additional Information:
Jon
F.
Carlson
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email:
jfc@math.uga.edu
Sunil
K.
Chebolu
Affiliation:
Department of Mathematics, Illinois State University, Normal, Illinois 61790
Email:
schebol@ilstu.edu
Ján
Minác
Affiliation:
Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
Email:
minac@uwo.ca
DOI:
10.1090/S0002-9939-09-09826-8
PII:
S 0002-9939(09)09826-8
Keywords:
Tate cohomology,
generating hypothesis,
stable module category,
ghost map,
almost split sequence.
Received by editor(s):
June 12, 2008,
Received by editor(s) in revised form:
October 21, 2008
Posted:
February 6, 2009
Additional Notes:
The first author is partially supported by a grant from the NSF
The third author is supported by the NSERC
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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