Varieties of subalgebras and endotrivial modules (Q6169072)

Let \(\mathfrak{g}\) be a restricted Lie algebra over a field \(k\) of odd characteristic. A \(\mathfrak{g}\)-module \(M\) is said to be endotrivial if \(\hom_{k}(M, M) \cong M \otimes M^{\star}\) is the direct sum of the trivial module and a projective one. \par In the paper under review the authors provide a description of the endotrivial modules in the case that \(\mathfrak{g}\) is supersolvable. If additionally \(k\) is algebraically closed, this yields a classification of the indecomposable modules of constant Jordan type with one non-projective block.