On the representations of a family of pointed Hopf algebras

Abstract

For each $\ell\geq 1$ and $\lambda,\mu\in\Bbbk$, 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 $\mathcal{FK}_3\#\Bbbk \mathbb{G}_{3,\ell}$, where $\mathcal{FK}_3$ is the Fomin-Kirillov algebra and $\mathbb{G}_{3,\ell}$ 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.