Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Octonions, exceptional Jordan algebra and the role of the group F_4 in
  particle physics   Normed division rings are reviewed in the more general framework of
composition algebras that include the split (indefinite metric) case. The
Jordan - von Neumann - Wigner classification of finite dimensional Jordan
algebras is outlined with special attention to the 27 dimensional exceptional
Jordan algebra J. The automorphism group F_4 of J and its maximal Borel - de
Siebenthal subgroups are studied in detail and applied to the classification of
fundamental fermions and gauge bosons. Their intersection in F_4 is
demonstrated to coincide with the gauge group of the Standard Model of particle
physics. The first generation's fundamental fermions form a basis of primitive
idempotents in the euclidean extension of the Jordan subalgebra JSpin_9 of J.

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex