The upper triangular solutions to the three-state constant quantum Yang-Baxter equation

Details The upper triangular solutions to the three-state constant quantum Yang-Baxter equation The upper triangular solutions to the three-state constant quantum Yang-Baxter equation

1993-06-14

arxiv.org/abs/solv-int/9306001v2

Physics

High Energy Physics

High Energy Physics - Theory

24 Pages in LaTeX

Scientific paper

10.1088/0305-4470/26/23/044

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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