Braids and Permutations
| dc.creator | Lin, Vladimir | |
| dc.date | 2004-04-29 | |
| dc.date.accessioned | 2026-07-07T05:07:48Z | |
| dc.date.available | 2026-07-07T05:07:48Z | |
| dc.description | E. Artin described all irreducible representations of the braid group B_k to the symmetric group S(k). We strengthen some of his results and, moreover, exhibit a complete picture of homomorphisms of B_k to S(n) for n<2k+1. We show that the image of such ahomomorphism f is cyclic whenever either (*) n<k\ne 4 or (**) f is irreducible and 6<k<n<2k. For k>6 there exist, up to conjugation, exactly 3 irreducible representations of B_k into S(2k) with non-cyclic images but they all are imprimitive. We use these results to prove that for n<k\ne 4 the image of any homomorphism from B_k to B_n is cyclic, whereas any endomorphism of B_k with non-cyclic image preserves the pure braid group PB_k. We prove also that for k>4 the intersection PB_k\cap B'_k of PB_k with the commutator subgroup B'_k=[B_k,B_k] is a completely characteristic subgroup of B'_k. | |
| dc.description | 110pp | |
| dc.identifier | https://arxiv.org/abs/math/0404528 | |
| dc.identifier | http://arxiv.org/abs/math/0404528 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71005 | |
| dc.subject | Group Theory | |
| dc.subject | 55P | |
| dc.title | Braids and Permutations | |
| dc.type | text |