Indecomposable modules of 2-step solvable Lie algebras in arbitrary characteristic

Abstract

Let F be an algebraically closed field and consider the Lie algebra = ⟨ x ⟩ ⋉ , where ad x acts diagonalizably on the abelian Lie algebra . Refer to a -module as admissible if [, ] acts via nilpotent operators on it, which is automatic if chr(F) = 0. In this article, we classify all indecomposable -modules U which are admissible as well as uniserial, in the sense that U has a unique composition series.