Finite GK-dimensional Nichols Algebras over the Infinite Dihedral Group

Abstract

We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GK-dimension for short, through the study of Nichols algebras over ${\mathbb{D}}_{\infty }$, the infinite dihedral group. We find all the irreducible Yetter-Drinfeld modules $V$ over ${\mathbb{D}}_{\infty }$, and determine which Nichols algebras $\mathcal{B}(V)$ of $V$ are finite GK-dimensional.