On the representations of a family of pointed Hopf algebras

For each $\mathrm{\ell }\ge 1$ and $\lambda ,\mu \in \mathbb{k}$, we study the representations of a family of pointed Hopf algebras ${\mathcal{A}}_{\lambda ,\mu }$. These arise as Hopf cocycle deformations of the graded algebra ${\mathcal{F}\mathcal{K}}_3\mathrm{\#}\mathbb{k}{\mathbb{G}}_{3,\mathrm{\ell }}$, where ${\mathcal{F}\mathcal{K}}_3$ is the Fomin-Kirillov algebra and ${\mathbb{G}}_{3,\mathrm{\ell }}$ is a given non-abelian finite group. We compute the simple modules, their projective covers and formulate a description of tensor products. We observe that our results are fundamentally different according to the shape of the Hopf cocycle involved in the deformation.