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

2022/05/02 by Hiss, Gerhard, Lassueur, Caroline
#20C20 #20C33 (Primary) 20C30 #20C34 (Secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2205.00958

Abstract

We investigate the source algebra class of a p-block with cyclic defect groups of the group algebra of a finite group. By the work of Linckelmann this class is parametrized by the Brauer tree of the block together with a sign function on its vertices and an endo-permutation module of a defect group. We prove that this endo-permutation module can be read off from the character table of the group. We also prove that this module is trivial for all cyclic p-blocks of quasisimple groups with a simple quotient which is a sporadic group, an alternating group, a group of Lie type in defining characteristic, or a group of Lie type in cross-characteristic for which the prime p is large enough in a certain sense.

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