English

On cohomological characterizations of endotrivial modules

Group Theory 2023-09-01 v1 Category Theory Representation Theory

Abstract

Given a general finite group GG, there are various finite categories whose cohomology theories are of great interests. Recently Balmer and Grodal gave some new characterizations of the groups of endotrivial modules, via \v{C}ech cohomology and category cohomology, respectively, defined on certain orbit categories. These two seemingly different approaches share a common root in topos theory. We shall demonstrate the connection, which leads to a better understanding as well as new characterizations of the group of endotrivial modules.

Keywords

Cite

@article{arxiv.2308.16838,
  title  = {On cohomological characterizations of endotrivial modules},
  author = {Fei Xu and Chenyou Zheng},
  journal= {arXiv preprint arXiv:2308.16838},
  year   = {2023}
}