Mathematical Research Letters

Volume 24 (2017)

Number 3

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

Pages: 619 – 643

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n3.a2

Authors

Nicolás Andruskiewitsch (FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Argentina)

Iván Angiono (FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Argentina)

Fiorela Rossi Bertone (FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Argentina)

Abstract

Let $\mathcal{B}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\mathfrak{q}$. We consider the graded dual $\mathcal{L}_{\mathfrak{q}}$ of the distinguished pre-Nichols algebra $\widetilde{\mathcal{B}}_{\mathfrak{q}}$ from [A3] and the quantum divided power algebra $\mathcal{U}_{\mathfrak{q}}$, a suitable Drinfeld double of $\mathcal{L}_{\mathfrak{q}} \# \mathbf{k} \mathbb{Z}^{\theta}$. We provide basis and presentations by generators and relations of $\mathcal{L}_{\mathfrak{q}}$ and $\mathcal{U}_{\mathfrak{q}}$, and prove that they are noetherian and have finite Gelfand–Kirillov dimension.

2010 Mathematics Subject Classification

16Wxx

Full Text (PDF format)

Received 19 January 2015

Published 1 September 2017