Low-dimensional representations of the three component loop braid group
Motivated by physical and topological applications, we study representations of the group LB3 of motions of 3 unlinked oriented circles in R3. Our point of view is to regard the three strand braid group B3 as a subgroup of LB3 and study the problem of extending B3 representations. We introduce the n...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/51849 |
| Acceso en línea: | http://hdl.handle.net/11336/51849 |
| Access Level: | acceso abierto |
| Palabra clave: | REPRESENTATIONS LOOP BRAID GROUP BRAID GROUP STANDARD EXTENSION LOW DIMENSIONAL IRREDUCIBLE REPRESENTATIONS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Motivated by physical and topological applications, we study representations of the group LB3 of motions of 3 unlinked oriented circles in R3. Our point of view is to regard the three strand braid group B3 as a subgroup of LB3 and study the problem of extending B3 representations. We introduce the notion of a standard extension and characterize B3 representations admitting such an extension. In particular we show, using a classification result of Tuba and Wenzl [Pacific J. Math. 197, 491-510 (2001)], that every irreducible B3 representation of dimension at most 5 has a (standard) extension. We show that this result is sharp by exhibiting an irreducible 6-dimensional B3 representation that has no extensions (standard or otherwise). We obtain complete classifications of (1) irreducible 2-dimensional LB3 representations, (2) extensions of irreducible 3-dimensional B3 representations, and (3) irreducible LB3 representations whose restriction to B3 has abelian image. |
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