Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classification of orbits on certain exceptional Jordan algebra under
  the automorphism group   Let $\mathcal{J}^1$ be the real form of complex simple Jordan algebra with
the automorphism group $G$ of type $F_{4(-20)}$. Explicitly, we give the orbit
decomposition of $\mathcal{J}^1$ under the action of $G$ and determine the Lie
group structure of stabilizer for each $G$-orbit on $\mathcal{J}^1$.

5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th