Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Trivial Extensions of the 3D-Poincar\'e Algebra and Fractional
  Supersymmetry for Anyons   Non-trivial extensions of the three dimensional Poincar\'e algebra, beyond
the supersymmetric one, are explicitly constructed. These algebraic structures
are the natural three dimensional generalizations of fractional supersymmetry
of order $F$ already considered in one and two dimensions. Representations of
these algebras are exhibited, and unitarity is explicitly checked. It is then
shown that these extensions generate symmetries which connect fractional spin
states or anyons. Finally, a natural classification arises according to the
decomposition of $F$ into its product of prime numbers leading to sub-systems
with smaller symmetries.

37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc