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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.21690 |
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| _version_ | 1866909904773578752 |
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| author | Doikou, Anastasia |
| author_facet | Doikou, Anastasia |
| contents | We introduce the special set-theoretic Yang-Baxter algebra and show that it is a Hopf algebra subject to certain conditions. The associated universal R-matrix is also obtained via an admissible Drinfel'd twist. The structure of braces emerges naturally in this context by requiring the special set-theoretic Yang-Baxter algebra to be a Hopf algebra and a quasi-triangular bialgebra after twisting. The fundamental representation of the universal R-matrix yields the familiar set-theoretic (combinatorial) solutions of the Yang-Baxter equation. We then apply the same Drinfel'd twist to the gl_n Yangian after introducing the augmented Yangian. We show that the augmented Yangian is also a Hopf algebra and we also obtain its twisted version. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial twists in gl_n Yangians Doikou, Anastasia Quantum Algebra High Energy Physics - Theory Mathematical Physics We introduce the special set-theoretic Yang-Baxter algebra and show that it is a Hopf algebra subject to certain conditions. The associated universal R-matrix is also obtained via an admissible Drinfel'd twist. The structure of braces emerges naturally in this context by requiring the special set-theoretic Yang-Baxter algebra to be a Hopf algebra and a quasi-triangular bialgebra after twisting. The fundamental representation of the universal R-matrix yields the familiar set-theoretic (combinatorial) solutions of the Yang-Baxter equation. We then apply the same Drinfel'd twist to the gl_n Yangian after introducing the augmented Yangian. We show that the augmented Yangian is also a Hopf algebra and we also obtain its twisted version. |
| title | Combinatorial twists in gl_n Yangians |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2504.21690 |