Endotrivial modules for finite groups of Lie type
-
Jon F Carlson
,
Nadia Mazza
Abstract
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
* = Homk (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.
© Walter de Gruyter
Articles in the same Issue
- Extension of structure groups of principal bundles in positive characteristic
- Phase transitions on Hecke C*-algebras and class-field theory over ℚ
- Existence results for a class of rate-independent material models with nonconvex elastic energies
- Endotrivial modules for finite groups of Lie type
- Solution to the inverse problem for upper asymptotic density
- Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space
- Cancellation in totally definite quaternion algebras
- Mesures et équidistribution sur les espaces de Berkovich
Articles in the same Issue
- Extension of structure groups of principal bundles in positive characteristic
- Phase transitions on Hecke C*-algebras and class-field theory over ℚ
- Existence results for a class of rate-independent material models with nonconvex elastic energies
- Endotrivial modules for finite groups of Lie type
- Solution to the inverse problem for upper asymptotic density
- Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space
- Cancellation in totally definite quaternion algebras
- Mesures et équidistribution sur les espaces de Berkovich
