How structure groups and monoids grow
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908547939303424 |
|---|---|
| author | Dietzel, Carsten Feingesicht, Edouard Lebed, Victoria |
| author_facet | Dietzel, Carsten Feingesicht, Edouard Lebed, Victoria |
| contents | The structure groups and monoids of set-theoretic solutions to the Yang-Baxter Equation can be regarded as deformations of free abelian groups resp. monoids. In this work, we obtain explicit formulae for the growth series of the structure groups and monoids of transposition and dihedral quandles, and of the structure groups of permutation quandles. These quandles provide important families of YBE solutions. The intricate nature of our formulae confirms that, while preserving many nice properties of free abelian groups, even the simplest structure groups and monoids are remarkably rich objects. We also establish some structural properties and easily computable normal forms for the monoids considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How structure groups and monoids grow Dietzel, Carsten Feingesicht, Edouard Lebed, Victoria Group Theory Combinatorics Number Theory Quantum Algebra Rings and Algebras 57K12, 16P90, 20B30, 20F05, 16T25 The structure groups and monoids of set-theoretic solutions to the Yang-Baxter Equation can be regarded as deformations of free abelian groups resp. monoids. In this work, we obtain explicit formulae for the growth series of the structure groups and monoids of transposition and dihedral quandles, and of the structure groups of permutation quandles. These quandles provide important families of YBE solutions. The intricate nature of our formulae confirms that, while preserving many nice properties of free abelian groups, even the simplest structure groups and monoids are remarkably rich objects. We also establish some structural properties and easily computable normal forms for the monoids considered. |
| title | How structure groups and monoids grow |
| topic | Group Theory Combinatorics Number Theory Quantum Algebra Rings and Algebras 57K12, 16P90, 20B30, 20F05, 16T25 |
| url | https://arxiv.org/abs/2509.16069 |