Finite GK-dimensional Nichols Algebras over the Infinite Dihedral Group

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.