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Geometry of Yang-Baxter matrix equations over finite fields (2506.17893v1)
Published 22 Jun 2025 in math.RA and math.AC
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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