A family of simple modules over the Rueda's algebras (Q2664505)

The Rueda's algebra, denoted by \(R\), is an associative algebra similar to the universal enveloping algebra of the Lie algebra \(\mathfrak{sl}_2\). The algebra \(R\) admits a natural triangular decomposition. The authors studied a class of nonweight modules over \(R\), which is free of rank-\(1\) when restricted to the zero part of \(R\). The main results of this paper include a classification of such modules up to isomorphism and determination of their irreducibility as well as submodule structure. As applications, some known results from literature on \(U(\mathfrak{h})\)-modules over the Lie algebra \(\mathfrak{sl}_2\) and Lie super-algebra \(\mathfrak{osp}(1|2)\) are reobtained.