The classification of endo-trivial modules.

DOI10.1007/s00222-004-0385-0zbMath1110.20004OpenAlexW1971392552MaRDI QIDQ706136

Jacques Thévenaz, Carlson, Jon F.

Publication date: 2 February 2005

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://infoscience.epfl.ch/record/130457/files/Final-classific.pdf

zbMATH Keywords

Dade groupsendo-permutation modulesfinite \(p\)-groupsrelative syzygiesendo-trivial modulesmaximal elementary Abelian subgroups

Mathematics Subject Classification ID

Modular representations and characters (20C20) Cohomology of groups (20J06) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15)

Related Items (33)

Endotrivial modules for finite groups via homotopy theory ⋮ Connected components of the category of elementary Abelian \(p\)-subgroups. ⋮ Universal deformation rings and generalized quaternion defect groups. ⋮ The group of endotrivial modules in the normal case. ⋮ Brauer’s generalized decomposition numbers and universal deformation rings ⋮ Endotrivial modules for nilpotent restricted Lie algebras ⋮ Modular representations of finite groups with trivial restriction to Sylow subgroups. ⋮ Universal deformation rings for the symmetric group \(S_5\) and one of its double covers. ⋮ Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup. ⋮ Torsion-free endotrivial modules. ⋮ Universal deformation rings and tame blocks ⋮ A tour of \(p\)-permutation modules and related classes of modules ⋮ Universal deformation rings and dihedral blocks with two simple modules. ⋮ Endotrivial modules for the Schur covers of the symmetric and alternating groups ⋮ The Dade group of a finite group. ⋮ Stable auto-equivalences for local symmetric algebras ⋮ Endotrivial modules for finite groups of Lie type \(A\) in nondefining characteristic ⋮ Universal deformation rings, endo-trivial modules, and semidihedral and generalized quaternion 2-groups ⋮ Toward a classification of endotrivial modules ⋮ Categorical constructions related to finite groups ⋮ Endotrivial modules for the general linear group in a nondefining characteristic. ⋮ Gluing representations via idempotent modules and constructing endotrivial modules. ⋮ \(p\)-groups with maximal elementary Abelian subgroups of rank 2. ⋮ Endotrivial representations of finite groups and equivariant line bundles on the Brown complex ⋮ Picard groups in triangular geometry and applications to modular representation theory ⋮ The Dade group of a \(p\)-group. ⋮ Universal deformation rings for the symmetric group \(S_4\). ⋮ Constructing endotrivial modules. ⋮ Jordan types for indecomposable modules of finite group schemes ⋮ Trivial-source endotrivial modules for sporadic groups ⋮ Endotrivial modules for $p$-solvable groups ⋮ The stable category and invertible modules for infinite groups ⋮ On endotrivial modules for Lie superalgebras

Uses Software

• Magma

Cites Work

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• Affirmative answer to a question of Feit.
• Endo-permutation modules over p-groups. I
• The Dade group of a metacyclic \(p\)-group
• The Dade group of (almost) extraspecial \(p\)-groups.
• The group of endo-permutation modules
• Constructing endotrivial modules.
• The classification of torsion endo-trivial modules.
• A construction of endo-permutation modules
• The Cohomology of Extraspecial Groups
• Tensor induction of relative syzygies
• Torsion endo-trivial modules

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