On finite GK-dimensional Nichols algebras of diagonal type: Rank 3 and Cartan type

Abstract

This paper contributes to the proof of the conjecture posed in AAH, stating that a Nicholsalgebra of diagonal type with finite Gelfand-Kirillov dimension has finite(generalized) root system. We prove the conjecture assuming that therank is 3 or that the braiding is of Cartan type.