Varieties of subalgebras and endotrivial modules

Abstract

Let (g,[p]) be a finite dimensional restricted Lie algebra over a perfect field k of characteristic p≥3. By combining methods from recent work of Benson-Carlson [4] with those of [10,16] we obtain a description of the endotrivial (g,[p])-modules in case the underlying Lie algebra g is supersolvable. For such g and algebraically closed k, this yields a classification of the indecomposable (g,[p])-modules of constant Jordan type with one non-projective block.