Mathematische Zeitschrift

, Volume 233, Issue 1, pp 165–178 | Cite as

Self-equivalences of stable module categories

  • Jon F. Carlson
  • Raphaël Rouquier
Original article


Let P be an abelian p-group, E a cyclic \(p'\)-group acting freely on P and k an algebraically closed field of characteristic \(p>0\). In this work, we prove that every self-equivalence of the stable module category of \(k[P\rtimes E]\) comes from a self-equivalence of the derived category of \(k[P\rtimes E]\). Work of Puig and Rickard allows us to deduce that if a block B with defect group P and inertial quotient E is Rickard equivalent to \(k[P\rtimes E]\), then they are splendidly Rickard equivalent. That is, Broué's original conjecture implies Rickard's refinement of the conjecture in this case. All of this follows from a general result concerning the self-equivalences of the thick subcategory generated by the trivial module.


General Result Module Category Stable Module Defect Group Trivial Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jon F. Carlson
    • 1
  • Raphaël Rouquier
    • 2
  1. 1.Department of Mathematics, University of Georgia, Athens, Georgia 30602, USA (e-mail: US
  2. 2.U.F.R. de Mathématiques, Université Denis Diderot et UMR 9994 du CNRS, 2 Place Jussieu, F-75251 Paris Cedex 05, France (e-mail: FR

Personalised recommendations