On the source algebra equivalence class of blocks with cyclic defect groups, II

2025/02/13 by Gerhard Hiß, Hiss, Gerhard, Caroline Lassueur +1
Mathematics · #20C15 #20C20 #20C33 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2502.09176

openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This series of papers is a contribution to the program of classifying p-blocks of finite groups up to source algebra equivalence, starting with the case of cyclic blocks. To any p-block B of a finite group with cyclic defect group D, Linckelmann associated an invariant W( B ), which is an indecomposable endo-permutation module over D, and which, together with the Brauer tree of B, essentially determines its source algebra equivalence class. In Parts II-IV of our series of papers, we classify, for odd p, those endo-permutation modules of cyclic p-groups arising from p-blocks of quasisimple groups. In the present Part II, we reduce the desired classification for the quasisimple classical groups of Lie type B, C, and D to the corresponding objective for the general linear and unitary groups; the classification is completed for the latter groups.

Related

• On the source algebra equivalence class of blocks with cyclic defect groups, I
• Trivial source characters in blocks with cyclic defect groups
• The classification of the trivial source modules in blocks with cyclic\n defect groups
• The source permutation module of a block of a finite group algebra
• p-permutation equivalences between blocks of group algebras