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Thick Subcategories of the Relative Stable Category

  • Jon F. CarlsonEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)

Abstract

Let G be a finite group and k an algebraically closed field of characteristic \(p > 0\). Let \({\mathcal H}\) be a collection of p-subgroups of G. We investigate the relative stable category \(\mathbf{stmod}_{\mathcal H}(kG)\) of finitely generated modules modulo \({\mathcal H}\)-projective modules. Triangles in this category correspond to \({\mathcal H}\)-split sequences. Hence, compared to the ordinary stable category, there are fewer triangles and more thick subcategories. Our interest is in the spectrum of the category and its relationship to the induction functor. In some cases, the spectrum is not noetherian.

1991 Mathematics Subject Classification

20C20 (primary) 20J06 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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