Endotrivial Modules for Finite Group Schemes

2009/06/17 by Jon F. Carlson, Jon Carlson, Carlson, Jon F. +2 · 1 citation
Mathematics · #20C20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C20

paper · pdf · doi:10.48550/arxiv.0906.3145

arxiv created 2009/06/17 · openalex publication_date 2009/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that if G is a finite group then the group of endotrivial modules is finitely generated. In this paper we investigate endotrivial modules over arbitrary finite group schemes. Our results can be applied to computing the endotrivial group for several classes of infinitesimal group schemes which include the Frobenius kernels of parabolic subgroups, and their unipotent radicals(for reductive algebraic groups). For G reductive, we also present a classification of simple, induced/Weyl and tilting modules (G-modules) which are endotrivial over the Frobenius kernel G_r of G.

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