Irreducible representations of pointed Hopf algebras of type $A_2$

Abstract

We classify the irreducible representations of a family of finite-dimensional pointed liftings $H_{\lambda }$ of the Nichols algebra associated with the diagram $A_2$ with parameter $q=-1$. We show that these algebras have infinite representation type and construct an indecomposable $H_{\lambda }$-module of dimension $n$ for each $n\in \mathbb{N}$. Finally, we study a semisimple category $\underline{\mathrm{Rep}}{H}_{\lambda }$ arising as a quotient of $\mathrm{Rep}{H}_{\lambda }$.

23 pages