Geometry of Yang-Baxter matrix equations over finite fields

2025/06/22 by Chen, Yin, Zhu, Shaoping
#13P25 #14A25 #15A24 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2506.17893

Abstract

Let A be a 2× 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.

Citations

• Modular matrix invariants under some transpose actions
• Invariant theory and coefficient algebras of Lie algebras
• Involutive Yang-Baxter Groups
• Mixed Bruhat operators and Yang-Baxter equations for Weyl groups

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