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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.18685 |
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| _version_ | 1866914532767563776 |
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| author | de Leeuw, Marius Posch, Vera |
| author_facet | de Leeuw, Marius Posch, Vera |
| contents | In this paper, we complete the classification of 4 x 4 solutions of the Yang-Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang-Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R-matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R-matrices satisfy a modified Yang-Baxter equation instead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All 4 x 4 solutions of the quantum Yang-Baxter equation de Leeuw, Marius Posch, Vera Mathematical Physics Statistical Mechanics High Energy Physics - Theory Exactly Solvable and Integrable Systems In this paper, we complete the classification of 4 x 4 solutions of the Yang-Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang-Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R-matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R-matrices satisfy a modified Yang-Baxter equation instead. |
| title | All 4 x 4 solutions of the quantum Yang-Baxter equation |
| topic | Mathematical Physics Statistical Mechanics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2411.18685 |