The quantum divided power algebra of a finite-dimensional Nichols algebra of diagonal type

Abstract

Let Bq be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q. We consider the graded dual Lq of the distinguished pre-Nichols algebra Bq from [A3] and the quantum divided power algebra Uq, a suitable Drinfeld double of Lq#kZθ. We provide basis and presentations by generators and relations of Lq and Uq, and prove that they are noetherian and have finite Gelfand-Kirillov dimension.