Hopf actions of Bosonizations on path algebras of quivers

In this dissertation we continue work of Kinser and Oswald \cite{kinser2021hopf} which classified Hopf actions of several families of Hopf algebras related to $U_q(\mathfrak{sl}_2)$ on path algebras of quivers, restricting attention to actions which preserve the ascending filtration of the path algebra by path length. In particular, we use their results on actions of Taft algebras to study actions of Bosonizations of quantum linear space with the group algebras, denoted $B:=\mathcal{R}(g_1,...,g_\theta,\chi_1,...,\chi_\theta)\#\kk G$. For these Bosonizations, we follow the exposition of Cline and Gaddis \cite{cline2020actions}.