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 out of 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-Procesi quantum groups. There are two new examples, one of which can be thought of as $G_2$ at a third root of one.

34 pages

References in corpus (1)

• Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type

Cited by in corpus (1)

• Rank 4 Nichols Algebras of Pale Braidings