Hecke algebras for set-theoretical solutions to the Yang--Baxter equation
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910680732401664 |
|---|---|
| author | Feingesicht, Edouard |
| author_facet | Feingesicht, Edouard |
| contents | We define a concept of Hecke algebra for structure groups of set-theoretical solutions to the Yang--Baxter equation. As a comparison to Artin--Tits groups of spherical type, we study some properties of this construction, while also highlighting some differences that appear, which shows a difference between finite Coxeter groups and the "Coxeter-like" group introduced by Dehornoy. We also relate this definition to known constructions on solutions (retractions). Finally, we study a particular case related to Torus Knot groups and Complex Reflexion groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hecke algebras for set-theoretical solutions to the Yang--Baxter equation Feingesicht, Edouard Quantum Algebra Group Theory 16T25, 20N02, 20C08 We define a concept of Hecke algebra for structure groups of set-theoretical solutions to the Yang--Baxter equation. As a comparison to Artin--Tits groups of spherical type, we study some properties of this construction, while also highlighting some differences that appear, which shows a difference between finite Coxeter groups and the "Coxeter-like" group introduced by Dehornoy. We also relate this definition to known constructions on solutions (retractions). Finally, we study a particular case related to Torus Knot groups and Complex Reflexion groups. |
| title | Hecke algebras for set-theoretical solutions to the Yang--Baxter equation |
| topic | Quantum Algebra Group Theory 16T25, 20N02, 20C08 |
| url | https://arxiv.org/abs/2411.00695 |