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The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras

Part of: Low-dimensional topology Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  18 September 2018

L. Poulain d’Andecy  and
E. Wagner
L. Poulain d’Andecy
Affiliation:
Université de Reims Champagne-Ardenne, UFR Sciences Exactes et Naturelles, Laboratoire de Mathématiques, FRE 2011, Moulin de la Housse, BP 1039, 51100 Reims, France (loic.poulain-dandecy@univ-reims.fr)
E. Wagner
Affiliation:
Université de Bourgogne–Franche-Comté, Institut de Mathématiques de Bourgogne, UMR 5584, 21000 Dijon, France (emmanuel.wagner@u-bourgogne.fr)
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Abstract

We describe completely the link invariants constructed using Markov traces on the Yokonuma–Hecke algebras in terms of the linking matrix and the Hoste–Ocneanu–Millett–Freyd–Lickorish–Yetter–Przytycki–Traczyk (HOMFLY-PT) polynomials of sublinks.

Keywords

Yokonuma-Hecke algebrasMarkov traceslinking numbers

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 20C08: Hecke algebras and their representations 20F36: Braid groups; Artin groups 57M25: Knots and links in $S^3$
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 6 , December 2018 , pp. 1269 - 1278
Copyright
Copyright © Royal Society of Edinburgh 2018 

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