Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutative Hopf structures over a loop   Let $k$ be an algebraically closed field of characteristic $p>0$. For a loop
$\circlearrowleft$, denote its path coalgebra by $k\circlearrowleft$. In this
paper, all the finite-dimensional commutative Hopf algebras over the sub
coalgebras of $k\circlearrowleft$ are given. As a direct consequence, all the
commutative infinitesimal groups $\mathcal{G}$ with
dim$_{k}$Lie$(\mathcal{G})=1$ are classified.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn