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Finite GK-dimensional Nichols Algebras over the Infinite Dihedral Group (2203.10535v2)
Published 20 Mar 2022 in math.QA and math.RA
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.