English

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

Representation Theory 2025-12-08 v3 Group Theory

Abstract

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

Keywords

Cite

@article{arxiv.2502.09176,
  title  = {On the source algebra equivalence class of blocks with cyclic defect groups, II},
  author = {Gerhard Hiss and Caroline Lassueur},
  journal= {arXiv preprint arXiv:2502.09176},
  year   = {2025}
}

Comments

35 pages, part II of a series of 4 articles, very minor correction to v2

R2 v1 2026-06-28T21:42:54.306Z