Subgroups of braid groups generated by Birman-Ko-Lee generators
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915796634042368 |
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| author | Nordskova, Anya Bergh, Michel Van den |
| author_facet | Nordskova, Anya Bergh, Michel Van den |
| contents | We define a Young subgroup of the braid group as a subgroup generated by an arbitrary subset of the Birman-Ko-Lee generators. We give an intrinsic description of such subgroups which yields, in particular, an easy criterion to decide membership. We also give an algorithm to write an element of a Young subgroup as a product of the generators. Our methods are based on analyzing the Hurwitz action on tuples over free groups via a diagrammatic approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subgroups of braid groups generated by Birman-Ko-Lee generators Nordskova, Anya Bergh, Michel Van den Group Theory Rings and Algebras 20F36 We define a Young subgroup of the braid group as a subgroup generated by an arbitrary subset of the Birman-Ko-Lee generators. We give an intrinsic description of such subgroups which yields, in particular, an easy criterion to decide membership. We also give an algorithm to write an element of a Young subgroup as a product of the generators. Our methods are based on analyzing the Hurwitz action on tuples over free groups via a diagrammatic approach. |
| title | Subgroups of braid groups generated by Birman-Ko-Lee generators |
| topic | Group Theory Rings and Algebras 20F36 |
| url | https://arxiv.org/abs/2410.13544 |