Iterated Hopf Ore Extensions over Group Rings

We introduce and study a class of Hopf algebras $H(G,\chi ,\eta ,b,c,\beta )$ which are two-step Ore extensions of a group algebra $\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as generalized Taft algebras and Hopf algebras related to ${\mathfrak{s}\mathfrak{l}}_2$ constructed by Wang, Wu, and Tan. We analyze the ring theoretical properties of these algebras and classify all finite dimensional simple modules over them.