Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $R$-triviality of $F_4$   It is known that simple algebraic groups of type $F_4$ defined over a field
$k$ are precisely the full automorphism groups of Albert algebras over $k$. We
explore $R$-triviality for the group $\text{\bf Aut}(A)$ when $A$ is an Albert
algebra. In this paper, we consider the case when $A$ is an Albert division
algebra, that arises from the first Tits construction. We prove that $\text{\bf
Aut}(A)$ is $R$-trivial, in the sense of Manin.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol