Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology rings of finite-dimensional pointed Hopf algebras over
  abelian groups   We show that the cohomology ring of a finite-dimensional complex pointed Hopf
algebra with an abelian group of group-like elements is finitely generated. Our
strategy has three major steps. We first reduce the problem to the finite
generation of cohomology of finite dimensional Nichols algebras of diagonal
type. For the Nichols algebras we do a detailed analysis of cohomology via the
Anick resolution reducing the problem further to specific combinatorial
properties. Finally, to check these properties we turn to the classification of
Nichols algebras of diagonal type due to Heckenberger. In this paper we
complete the verification of these combinatorial properties for major
parametric families, including Nichols algebras of Cartan and super types and
develop all the theoretical foundations necessary for the case-by-case
analysis. The remaining discrete families are addressed in a separate
publication. As an application of the main theorem we deduce finite generation
of cohomology for other classes of finite-dimensional Hopf algebras, including
basic Hopf algebras with abelian groups of characters and finite quotients of
quantum groups at roots of one.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys