On finite GK-dimensional Nichols algebras of diagonal type: rank 3 and Cartan type (2106.10143v1)

Abstract: This paper contributes to the proof of the conjecture posed in arXiv:1606.02521, stating that a Nichols algebra of diagonal type with finite Gelfand-Kirillov dimension has finite (generalized) root system. We prove the conjecture assuming that the rank is 3 or that the braiding is of Cartan type.