Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Type III_1 equilibrium states of the Toeplitz algebra of the affine
  semigroup over the natural numbers
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex