Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $q$-Inverting pairs of linear transformations and the $q$-tetrahedron
  algebra   As part of our study of the $q$-tetrahedron algebra $\boxtimes_q$ we
introduce the notion of a $q$-inverting pair. Roughly speaking, this is a pair
of invertible semisimple linear transformations on a finite-dimensional vector
space, each of which acts on the eigenspaces of the other according to a
certain rule. Our main result is a bijection between the following two sets:
  (i) the isomorphism classes of finite-dimensional irreducible
$\boxtimes_q$-modules of type 1;
  (ii) the isomorphism classes of $q$-inverting pairs.

13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th