On pointed Hopf algebras over dihedral groups.
Let \(k\) be an algebraically closed field of characteristic zero and let \(D_m\) be the dihedral group of order \(2m\). In this paper the authors complete the classification of finite-dimensional Nichols algebras over \(D_m\), where \(m=4t\), \(t\geq 3\). Based on the so-called Lifting Method due to N. Andruskiewitsch and H.-J. Schneider, this allows in turn to give the classification of finite-dimensional pointed Hopf algebras over \(k\) with group of group-like elements isomorphic to \(D_m\). The proof of the main result on Nichols algebras uses the classification of finite-dimensional Nichols algebras of diagonal type, done by \textit{I. Heckenberger} [in Adv. Math. 220, No. 1, 59-124 (2009; Zbl 1176.17011)].
scientific article