A family of simple modules over the Rueda's algebras

Abstract

The Rueda's algebras R(f,ς) (simply R) are a class of algebras similar to the universal enveloping algebra of sl2. We study the category H of R-modules whose objects are free of rank 1 when restricted to R0=C[H]. We classify the isomorphism classes of objects in H and determine the simplicity of these modules. As a result, we also give an explicit description of submodule structures and obtain new simple non-weight modules over R. In particular, we recover some results about U(h)-free modules over the Lie algebra sl2 obtained by J. Nilsson and over the Lie superalgebra osp(1|2) obtained by Y. Cai and K. Zhao.