On the source algebra equivalence class of blocks with cyclic defect groups, III
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909981171777536 |
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| author | Hiss, Gerhard Lassueur, Caroline |
| author_facet | Hiss, Gerhard Lassueur, Caroline |
| contents | 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 $\mathbf{B}$ of a finite group with cyclic defect group $D$, Linckelmann associated an invariant $W( \mathbf{B} )$, which is an indecomposable endo-permutation module over $D$, and which, together with the Brauer tree of~$\mathbf{B} $, essentially determines its source algebra equivalence class.
In Part II of our series, assuming that $p$ is an odd prime, we reduced the classification of the invariants $W( \mathbf{B} )$ arising from cyclic $p$-blocks $\mathbf{B}$ of quasisimple classical groups to the classification for cyclic $p$-blocks of quasisimple quotients of special linear or unitary groups. This objective is achieved in the present Part III. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01582 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the source algebra equivalence class of blocks with cyclic defect groups, III Hiss, Gerhard Lassueur, Caroline Representation Theory Group Theory 20C20, 20C15, 20C33 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 $\mathbf{B}$ of a finite group with cyclic defect group $D$, Linckelmann associated an invariant $W( \mathbf{B} )$, which is an indecomposable endo-permutation module over $D$, and which, together with the Brauer tree of~$\mathbf{B} $, essentially determines its source algebra equivalence class. In Part II of our series, assuming that $p$ is an odd prime, we reduced the classification of the invariants $W( \mathbf{B} )$ arising from cyclic $p$-blocks $\mathbf{B}$ of quasisimple classical groups to the classification for cyclic $p$-blocks of quasisimple quotients of special linear or unitary groups. This objective is achieved in the present Part III. |
| title | On the source algebra equivalence class of blocks with cyclic defect groups, III |
| topic | Representation Theory Group Theory 20C20, 20C15, 20C33 |
| url | https://arxiv.org/abs/2601.01582 |