Representation theory of the Drinfeld doubles of a family of Hopf algebras. (Q2576936)

The authors define by quiver and relations the Hopf algebras \(\Lambda_{n,d}\), which are the duals of the extended Taft Hopf algebras. The aim of the paper is to study representations of the Drinfeld double \({\mathcal D}(\Lambda_{n,d})\). The projective modules and the simple modules over \({\mathcal D}(\Lambda_{n,d})\) are described. A presentation by quiver and relations is given for \({\mathcal D}(\Lambda_{n,d})\), and then all the indecomposable representations are classified and the Auslander-Reiten quiver is described. Tensor products of representations are studied, including a complete description of the tensor product of two simple modules. Some examples of Hopf bimodules over \({\mathcal D}(\Lambda_{n,d})\) are given by using modules over \({\mathcal D}(\Lambda_{n,d})\).