The classification of the trivial source modules in blocks with cyclic\n defect groups

2019/08/21 by Gerhard Hiß, Hiss, Gerhard, Caroline Lassueur +1
Mathematics · #20C20 #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1908.07833

openalex publication_date 2019/08/21 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Relying on the classification of the indecomposable liftable modules in\narbitrary blocks with non-trivial cyclic defect groups we give a complete\nclassification of the trivial source modules lying in such blocks, describing\nin particular their associated path on the Brauer tree of the block in the\nsense of Janusz (1969). The appendix contains a description of the minimal\ndistance from an arbitrary non-projective indecomposable liftable module to the\nboundary of the stable Auslander-Reiten quiver of the block.\n

Related

• Trivial source characters in blocks with cyclic defect groups
• On the source algebra equivalence class of blocks with cyclic defect groups, I
• On blocks with trivial source simple modules
• On the source algebra equivalence class of blocks with cyclic defect groups, II
• Blocks with abelian defect groups of rank 2 and one simple module