dorsal/arxiv
View SchemaThe upper triangular solutions to the three-state constant quantum Yang-Baxter equation
| Authors | Jarmo Hietarinta |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9306001 |
| URL | https://arxiv.org/abs/solv-int/9306001 |
| DOI | 10.1088/0305-4470/26/23/044 |
Abstract
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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"abstract": "In this article we present all nonsingular upper triangular solutions to the\nconstant quantum Yang-Baxter equation\n$R_{j_1j_2}^{k_1k_2}R_{k_1j_3}^{l_1k_3}R_{k_2k_3}^{l_2l_3}=\nR_{j_2j_3}^{k_2k_3}R_{j_1k_3}^{k_1l_3}R_{k_1k_2}^{l_1l_2}$ in the three state\ncase, i.e. all indices ranging from 1 to 3. The upper triangular ansatz implies\n729 equations for 45 variables. Fortunately many of the equations turned out to\nbe simple allowing us to start breaking the problem into smaller ones. In the\nend we had a total of 552 solutions, but many of them were either inherited\nfrom two-state solutions or subcases of others. The final list contains 35\nnontrivial solutions, most of them new.",
"arxiv_id": "solv-int/9306001",
"authors": [
"Jarmo Hietarinta"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"doi": "10.1088/0305-4470/26/23/044",
"title": "The upper triangular solutions to the three-state constant quantum Yang-Baxter equation",
"url": "https://arxiv.org/abs/solv-int/9306001"
},
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