Free 2-step nilpotent Lie algebras and indecomposable modules

Abstract

Given an algebraically closed field $F$ of characteristic 0 and an $F$-vector space $V$, let $L(V)=V\oplus {\Lambda }^2(V)$ denote the free 2-step nilpotent Lie algebra associated to $V$. In this paper, we classify all uniserial representations of the solvable Lie algebra $\mathfrak{g}=⟨x⟩⋉L(V)$, where $x$ acts on $V$ via an arbitrary invertible Jordan block.

References in corpus (2)

• Irreducible $S{L}_{n+1}$--Representations remain Indecomposable restricted to some Abelian Subalgebras
• Indecomposable modules of solvable Lie algebras