Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypersymmetry: a Z_3-graded generalization of supersymmetry   We propose a generalization of non-commutative geometry and gauge theories
based on ternary Z_3-graded structures. In the new algebraic structures we
define, we leave all products of two entities free, imposing relations on
ternary products only. These relations reflect the action of the Z_3-group,
which may be either trivial, i.e. abc=bca=cab, generalizing the usual
commutativity, or non-trivial, i.e. abc=jbca, with j=e^{(2\pi i)/3}. The usual
Z_2-graded structures such as Grassmann, Lie and Clifford algebras are
generalized to the Z_3-graded case. Certain suggestions concerning the eventual
use of these new structures in physics of elementary particles are exposed.

5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th