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Jon F Carlson, Nadia Mazza, Daniel K Nakano

Endotrivial modules for finite groups of Lie type

1. Introduction

Let G be a finite group and k be a field of characteristic p > 0. An endotrivial kG-module is a finitely generated kG-module M whose k-endomorphism ring is isomorphic to a trivial module in the stable module category. That is, M is an endotrivial module provided where P is a projective kG-module. Now recall that as kG-modules, where M * = Hom_k (M, k) is the k-dual of M. Hence, the functor “ ” induces an equivalence on the stable module category and the collection of all endotrivial modules makes up a part of the Picard group of all stable equivalences of kG-modules. In particular, equivalence classes of endotrivial modules modulo projective summands form a group that is an essential part of the group of stable self-equivalences.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 06/2006
Pages: 93 - 119

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