Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Set-theoretic solutions of the Yang-Baxter equation and new classes of
  R-matrices   We describe several methods of constructing R-matrices that are dependent
upon many parameters, for example unitary R-matrices and R-matrices whose
entries are functions. As an application, we construct examples of R-matrices
with prescribed singular values.
  We characterise some classes of indecomposable set-theoretic solutions of the
quantum Yang-Baxter equation (QYBE) and construct R-matrices related to such
solutions. In particular, we establish a correspondence between one-generator
braces and indecomposable, non-degenerate involutive set-theoretic solutions of
the QYBE, showing that such solutions are abundant.
  We show that R-matrices related to involutive, non-degenerate solutions of
the QYBE have special form.
  We also investigate some linear algebra questions related to R-matrices.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat