Endotrivial modules for finite groups schemes II

zbMATH Open1287.20014arXiv1104.0226MaRDI QIDQ4914936

Daniel K. Nakano, Jon F. Carlson

Publication date: 15 April 2013

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 prove that for an arbitrary finite group scheme G, and for any fixed integer n > 0, there are only finitely many isomorphism classes of endotrivial modules of dimension n. This provides evidence to support the speculation that the group of endotrivial modules for a finite group scheme is always finitely generated. The result also has some applications to questions about lifting and twisting the structure of endotrivial modules in the case that G is an infinitesimal group scheme associated to an algebraic group.

Full work available at URL: https://arxiv.org/abs/1104.0226

zbMATH Keywords

cohomologyprojective modulessyzygiesnumerical stabilitysimply connected algebraic groupsFrobenius kernelsstable module categoriesendotrivial modulesfinite group schemestensor stabilitylifting module structuresstable liftings

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Group schemes (14L15)

Related Items (7)

Endo-monomial modules over \(p\)-groups and their classification in the Abelian case. ⋮ Endotrivial modules for nilpotent restricted Lie algebras ⋮ Toward a classification of endotrivial modules ⋮ Stable Green ring of the Drinfeld doubles of the generalised Taft algebras (corrections and new results) ⋮ Endotrivial modules for the symmetric and alternating groups ⋮ Endotrivial modules for finite groups of Lie type ⋮ On endotrivial modules for Lie superalgebras

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