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 generalize the exchange operator introduced by Milinski and Schneider for Coxeter groups in "Pointed indecomposable Hopf algebras over Coxeter groups".