Pointed Hopf algebras with classical Weyl groups. (Q2888831)

Let \(\mathbb S_n\) denote the symmetric group of degree \(n>2\) and let \(G=A\rtimes\mathbb S_n\) be a classical Weyl group, where \(A\subseteq\mathbb Z_2^n\). In the paper under review the authors give a necessary and sufficient condition for a Nichols algebra of an irreducible Yetter-Drinfeld module \(V\) over \(G\) supported by \(A\) to be finite dimensional. It is shown that Nichols algebras of irreducible Yetter-Drinfeld modules over \(G\) supported by \(\mathbb S_n\) are infinite dimensional, except in three cases. Related results on Nichols algebras over symmetric groups appeared in the paper [Ann. Mat. Pura Appl. (4) 190, No. 2, 225-245 (2011; Zbl 1234.16019)], by \textit{N. Andruskiewitsch, F. Fantino, M. Graña} and \textit{L. Vendramin}.