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

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Original languageEnglish
Publication statusE-pub ahead of print - 13 Feb 2025

Abstract

Linckelmann associated an invariant to a cyclic $p$-block of a finite group, which is an indecomposable endo-permutation module over a defect group, and which, together with the Brauer tree of the block, 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 classification for the general linear and unitary groups, which is also accomplished.

Keywords

    math.RT, math.GR, 20C20, 20C15, 20C33

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On the source algebra equivalence class of blocks with cyclic defect groups, II. / Hiss, Gerhard; Lassueur, Caroline.
2025.

Research output: Working paper/PreprintPreprint

Hiss G, Lassueur C. On the source algebra equivalence class of blocks with cyclic defect groups, II. 2025 Feb 13. Epub 2025 Feb 13. doi: 10.48550/arXiv.2502.09176
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