Iterated Hopf Ore Extensions Over Group Rings

ABSTRACT We introduce and study a class of Hopf algebras which are two‐step Ore extensions of a group algebra , parameterized by two elements and in . We show that the constructed Hopf algebras are pointed Noetherian Hopf algebra, whose Gelfand–Kirilov dimension is finite, in case is nilpotente‐by‐finite. We classify all irreducible representations over , in case is finitely generated Abelian and and have finite order, and determine their fusion rules in case (i.e., the derivation is zero). Our construction and certain Auslander–Schelter–Gorenstein quotients of it unify and generalize some known families of Hopf algebras such as the Hopf algebras related to constructed by Wang, Wu, and Tan, as well as generalized Taft algebras.