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

Ben-Michael Kohli; Bertrand Patureau-Mirand

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arXiv · 1606.02538

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

Ben-Michael Kohli·Bertrand Patureau-Mirand

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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.

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BibTeX RIS

Ben-Michael Kohli, Bertrand Patureau-Mirand. 2016-06-08. Other quantum relatives of the Alexander polynomial through the Links-Gould invariants. https://arxiv.org/abs/1606.02538

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