On cohomological characterizations of endotrivial modules
Group Theory
2023-09-01 v1 Category Theory
Representation Theory
Abstract
Given a general finite group , 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}
}