The classification of torsion endo-trivial modules
| dc.creator | Carlson, Jon F. | |
| dc.creator | Thevenaz, Jacques | |
| dc.date | 2007-06-27 | |
| dc.date.accessioned | 2026-07-07T08:12:44Z | |
| dc.date.available | 2026-07-07T08:12:44Z | |
| dc.description | This paper is a major step in the classification of endotrivial modules over p-groups. Let G be a finite p-group and k be a field of characteristic p. A kG-module M is an endo-trivial module if {\End_k(M)\cong k\oplus F} as kG-modules, where F is a free module. The classification of endo-trivial modules is the crucial step for understanding the more general class of endo-permutation modules. The endo-permutation modules play an important role in module theory, in particular as source modules, and in block theory where they appear in the description of source algebras. Endo-trivial modules are also important in the study of both derived equivalences and stable equivalences of group algebras and block algebras. The collection of isomorphism classes of endo-trivial modules modulo projectives is an abelian group under tensor product. The main result of this paper is that this group is torsion free except in the case that G is cyclic, quaternion or semi-dihedral. Hence for any p-group which is not cyclic, quaternion or semi-dihedral and any finitely generated kG-module M, if M \otimes_k M \otimes_k ... \otimes_k M \cong k \oplus P for some projective module P and some finite number of tensor products, then M \cong k \oplus Q for some projective module Q. The proof uses a reduction to the cases in which G is an extraspecial or almost extraspecial p-group, proved in a previous paper of the authors, and makes extensive use of the theory of support varieties for modules. | |
| dc.description | 61 pages, published version | |
| dc.identifier | https://arxiv.org/abs/0706.4081 | |
| dc.identifier | http://arxiv.org/abs/0706.4081 | |
| dc.identifier | Ann. of Math. (2) 162 (2005), no. 2, 823--883 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132554 | |
| dc.subject | Group Theory | |
| dc.title | The classification of torsion endo-trivial modules | |
| dc.type | text |