Hopf algebras. We organize the paper as follows. In this section, we recall some properties of projective cover and representation theories of Artin algebras, and integrals in a finite dimensional Hopf algebra, which can be found in [@Aus95; @Igl09; @Mon93]. In Section \[2\], we introduce the Hopf algebras $\mathcal{B}(V)\# kG$ and its “lifting" $H(\lambda,\mu)$ given in [@Cib09], and investigate some properties of $H(\lambda,\mu)$. We show that $\mathcal{B}(V)\# kG$ and $H(\lambda,\mu)$ are symmetric algebras. In Section \[3\], we describe the simple modules over $H(\lambda,\mu)$. Then we consider the tensor products of simple module by using the idea of [@Ch00] and prove that the tensor product of any two simple modules is indecomposable. Through computing idempotent elements, we find the projective covers of these simple modules. In Section \[4\], we compute the extensions of some simple modules over the Hopf algebras and prove that these Hopf algebras are of wild representation type.

Now we recall some general facts about the representation theory of a finite dimensional algebra. Let $A$ be a finite dimensional algebra over an algebraically closed field and $\widehat{A}=\{S_1,\cdots,S_n\}$ be a complete set of non-isomorphic simple $A$-modules. Let $P(S)$ denote the projective cover of $S$, $S\in\widehat{A}$. It is well-known that 