The classification of the cyclic $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$--modules
arXiv:1508.07203
Abstract
In this paper we classify all the cyclic finite dimensional indecomposable\\ modules of the perfect Lie algebras $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$, given by the semidirect sum of the simple Lie algebra with its standard representation. Furthermore, using the embeddings of the Lie algebras $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$ in , we show that any finite dimensional irreducible module of restricted to $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$ is a cyclic module and that any cyclic $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$--modules can be constructed as quotient module of the restriction to $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$ of some finite dimensional irreducible --modules. This explicit realization of the cyclic $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$--modules plays a role in their classification.