Other quantum relatives of the Alexander polynomial through the Links-Gould invariants

Ben-Michael Kohli 1 Bertrand Patureau-Mirand 2
2 LMBA_UBS
LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
Abstract : Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to $U_q sl(2)$ at fourth roots of unity, or by considering the super Hopf algebra $U_q gl(1|1)$. In this paper, we show these Hopf algebras share properties with the $-1$ specialization of $U_q gl(n|1)$ leading to the proof of a conjecture of David De Wit, Atsushi Ishii and Jon Links on the Links-Gould invariants.
Type de document :
Pré-publication, Document de travail
13 pages. 2016
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https://hal.archives-ouvertes.fr/hal-01329298
Contributeur : Bertrand Patureau Mirand <>
Soumis le : jeudi 9 juin 2016 - 04:19:54
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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  • HAL Id : hal-01329298, version 1
  • ARXIV : 1606.02538

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Ben-Michael Kohli, Bertrand Patureau-Mirand. Other quantum relatives of the Alexander polynomial through the Links-Gould invariants. 13 pages. 2016. <hal-01329298>

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