Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The upper triangular solutions to the three-state constant quantum
  Yang-Baxter equation   In this article we present all nonsingular upper triangular solutions to the
constant quantum Yang-Baxter equation
$R_{j_1j_2}^{k_1k_2}R_{k_1j_3}^{l_1k_3}R_{k_2k_3}^{l_2l_3}=
R_{j_2j_3}^{k_2k_3}R_{j_1k_3}^{k_1l_3}R_{k_1k_2}^{l_1l_2}$ in the three state
case, i.e. all indices ranging from 1 to 3. The upper triangular ansatz implies
729 equations for 45 variables. Fortunately many of the equations turned out to
be simple allowing us to start breaking the problem into smaller ones. In the
end we had a total of 552 solutions, but many of them were either inherited
from two-state solutions or subcases of others. The final list contains 35
nontrivial solutions, most of them new.

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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: math