Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite quantum groups over abelian groups of prime exponent   Since the discovery of quantum groups (Drinfeld, Jimbo) and finite
dimensional variations thereof (Lusztig, Manin), these objects were studied
from different points of view and had many applications. The present paper is
part of a series where we intend to show that important classes of Hopf
algebras are quantum groups and therefore belong to Lie theory. One of our main
results is the explicit construction of a general family of pointed Hopf
algebras from Dynkin diagrams. All the Frobenius-Lusztig kernels and their
parabolic subalgebras belong to this family, but in addition we get many new
examples. We show that any finite dimensional pointed Hopf algebra with group
of prime exponent (greater than 17) is indeed in this family. An important step
in the proof follows from a another result, where we show that a wide family of
finite dimensional pointed Hopf algebras is generated by group-like and
skew-primitive elements, giving additional support to a conjecture in our
previous paper "Finite quantum groups and Cartan matrices", Adv. Math. 154
(2000), 1--45.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
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The categories of this paper are: eess