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| Originalsprache | Englisch |
|---|---|
| Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 13 Feb. 2025 |
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2025.
Publikation: Arbeitspapier/Preprint › Preprint
}
TY - UNPB
T1 - On the source algebra equivalence class of blocks with cyclic defect groups, II
AU - Hiss, Gerhard
AU - Lassueur, Caroline
N1 - 35 pages, part II of a series of 4 articles
PY - 2025/2/13
Y1 - 2025/2/13
N2 - 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.
AB - 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.
KW - math.RT
KW - math.GR
KW - 20C20, 20C15, 20C33
U2 - 10.48550/arXiv.2502.09176
DO - 10.48550/arXiv.2502.09176
M3 - Preprint
BT - On the source algebra equivalence class of blocks with cyclic defect groups, II
ER -