Geometry of Yang-Baxter Matrix Equations over Finite Fields
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.
Fields of Study & Subjects
Advanced Topics in Algebra
Matrix Theory and Algorithms
Random Matrices and Applications
Publication details
- Journal / source
- Experimental Mathematics
- Publisher
- Informa UK Limited
- Pages
- 1–29
- Publication date
- 11 April 2026
- Language
- EN