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arXiv · 2411.18685

All 4 x 4 solutions of the quantum Yang-Baxter equation

Marius de Leeuw·Vera Posch
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Abstract

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.

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Marius de Leeuw, Vera Posch. 2024-11-27. All 4 x 4 solutions of the quantum Yang-Baxter equation. https://arxiv.org/abs/2411.18685

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