Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exceptional quantum algebra for the standard model of particle physics   The exceptional euclidean Jordan algebra of 3x3 hermitian octonionic
matrices, appears to be tailor made for the internal space of the three
generations of quarks and leptons. The maximal rank subgroup of its
automorphism group F4 that respects the lepton-quark splitting is the product
of the colour SU(3) with an "electroweak" SU(3) factor. Its intersection with
the automorphism group Spin(9) of the special Jordan subalgebra J, associated
with a single generation of fundamental fermions, is precisely the symmetry
group S(U(3)xU(2)) of the Standard Model. The Euclidean extension of J involves
32 primitive idempotents giving the states of the first generation fermions.
The triality relating left and right Spin(8) spinors to 8-vectors corresponds
to the Yukawa coupling of the Higgs boson to quarks and leptons.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci