Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type

Abstract

We study pre-Nichols algebras of quantum linear spaces and of Cartan type with finite GK-dimension. We prove that except for a short list of exceptions involving only roots of order 2, 3, 4, 6, any such pre-Nichols algebra is a quotient of the distinguished pre-Nichols algebra introduced by Angiono generalizing the De Concini-Kac-Procesi quantum groups. There are two new examples, one of which can be thought of as G 2 G_2 at a third root of one.