Geometry of Yang-Baxter matrix equations over finite fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917224209448960 |
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| author | Chen, Yin Zhu, Shaoping |
| author_facet | Chen, Yin Zhu, Shaoping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry of Yang-Baxter matrix equations over finite fields Chen, Yin Zhu, Shaoping Rings and Algebras Commutative Algebra 15A24, 13P25, 14A25 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. |
| title | Geometry of Yang-Baxter matrix equations over finite fields |
| topic | Rings and Algebras Commutative Algebra 15A24, 13P25, 14A25 |
| url | https://arxiv.org/abs/2506.17893 |