Varieties of subalgebras and endotrivial modules

TL;DR

This paper characterizes endotrivial modules over supersolvable restricted Lie algebras using a combination of recent algebraic methods, advancing understanding of module varieties in this algebraic context.

Contribution

It provides a new description of endotrivial modules for supersolvable restricted Lie algebras by integrating recent techniques from Benson-Carlson and others.

Findings

Endotrivial modules are classified for supersolvable restricted Lie algebras.

The approach combines methods from recent algebraic research.

Results extend the understanding of module varieties in Lie algebra theory.

Abstract

Let $(\mathfrak{g},[p])$ be a finite dimensional restricted Lie algebra over a perfect field $\mathbbm{k}$ of characteristic $p\!\ge \!3$. By combining methods from recent work of Benson-Carlson \cite{BC20} with those of \cite{CF21,Fa17} we obtain a description of the endotrivial $(\mathfrak{g},[p])$-modules in case $\mathfrak{g}$ is supersolvable.