Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-abelian group type

We present a divisibility relation for the dimensions and Hilbert series of certain classes of Nichols algebras of non-abelian group type, which generalizes Nichols algebras over Coxeter groups with constant cocycle −1. For this we introduce three groups of isomorphisms acting on Nichols algebras, which generalizes the exchange operator introduced by Milinski and Schneider (2000) [18] for Coxeter groups.