Algebras and Representation Theory

, Volume 4, Issue 4, pp 395–404 | Cite as

Phantom Maps and Purity in Modular Representation Theory, II

  • D. J. Benson
  • G. Ph. Gnacadja


In the second part of this paper, we use the theory described in the first part to construct an example of a counterintuitive phenomenon. We show how to produce examples of filtered systems in the stable module category stmod(kG) which do not lift to filtered systems in the module category mod(kG). Our main tool is the Extended Milnor Sequence, a five-term exact sequence which specializes to the classical Milnor sequence under certain countability conditions.

phantom maps modular representation theory extended Milnor sequence 


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    Benson, D. J. and Gnacadja, G. Ph.: Phantom maps and purity in modular representation theory, I, Fund. Math. 161 (1999), 37-91.Google Scholar
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    Christensen, J. D.: Ideals in triangulated categories: phantoms, ghosts and skeleta, Adv. In Math. 2 (1998), 284-339.Google Scholar
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    Gnacadja, G. Ph.: Phantom maps in the stable module category, J. Algebra 201 (1998), 686-702.Google Scholar
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    Jensen, C. U.: Les foncteurs dérivés de lim et leurs applications en théorie des modules, Lecture Notes in Math. 254, Springer, New York, 1972.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • D. J. Benson
    • 1
  • G. Ph. Gnacadja
    • 1
  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA e-mail

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