New Permutation Representations of the Braid Group
| dc.creator | Ferman, Amiel | |
| dc.creator | Nowik, Tahl | |
| dc.creator | Schwartz, Robert | |
| dc.creator | Teicher, Mina | |
| dc.date | 2008-11-26 | |
| dc.date.accessioned | 2026-07-07T12:04:26Z | |
| dc.date.available | 2026-07-07T12:04:26Z | |
| dc.description | We give a new infinite family of group homomorphisms from the braid group B_k to the symmetric group S_{mk} for all k and m \geq 2. Most known permutation representations of braids are included in this family. We prove that the homomorphisms in this family are non-cyclic and transitive. For any divisor l of m, 1\leq l < m, we prove in particular that if \frac{m}{l} is odd then there are 1 + \frac{m}{l} non-conjugate homomorphisms included in our family. We define a certain natural restriction on homomorphisms B_k to S_n, common to all homomorphisms in our family, which we term 'good', and of which there are two types. We prove that all good homomorphisms B_k to S_{mk} of type 1 are included in the infinite family of homomorphisms we gave. For m=3, we prove that all good homomorphisms B_k to S_{3k} of type 2 are also included in this family. Finally, we refute a conjecture made by Matei and Suciu regarding permutation representations of braids and give an updated conjecture. | |
| dc.description | 64pp | |
| dc.identifier | https://arxiv.org/abs/0811.4204 | |
| dc.identifier | http://arxiv.org/abs/0811.4204 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208132 | |
| dc.subject | Group Theory | |
| dc.subject | 20B30; 20B35; 57M99 | |
| dc.title | New Permutation Representations of the Braid Group | |
| dc.type | text |