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arXiv · 2506.17893

Geometry of Yang-Baxter matrix equations over finite fields

Yin Chen·Shaoping Zhu
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Abstract

Let $A$ be a $2\times 2$ matrix over a finite field and consider the Yang-Baxter matrix equation $XAX=AXA$ with respect to $A$. We use a method of computational ideal theory to explore the geometric structure of the affine variety of all solutions to this equation. In particular, we exhibit all solutions explicitly and determine cardinality formulas for these varieties.

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Yin Chen, Shaoping Zhu. 2025-06-22. Geometry of Yang-Baxter matrix equations over finite fields. https://arxiv.org/abs/2506.17893

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