Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The quantum divided power algebra of a finite-dimensional Nichols
  algebra of diagonal type   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 divided powers
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.

36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th