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

Authors: Ben-Michael Kohli and Bertrand Patureau-Mirand
Journal: Proc. Amer. Math. Soc. 145 (2017), 5419-5433
MSC (2010): Primary 57M27; Secondary 17B37
Published electronically: August 1, 2017
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Abstract: In 2006, Oleg Viro studied two interpretations of the (multivariable) Alexander polynomial understood as a quantum link invariant: either by considering the quasitriangular Hopf algebra associated to $ U_q{\mathfrak{sl}(2)}$ at fourth roots of unity, or by considering the super Hopf algebra $ U_q\mathfrak{gl}(1\vert 1)$. In this paper, we show these Hopf algebras share properties with the $ -1$ specialization of $ U_q\mathfrak{gl}(n\vert 1)$ leading to the proof of a conjecture by David De Wit, Atsushi Ishii and Jon Links on the Links-Gould invariants.

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Ben-Michael Kohli
Affiliation: IMB UMR5584, CNRS, Université Bourgogne Franche-Comté, F-21000 Dijon, France

Bertrand Patureau-Mirand
Affiliation: UMR 6205, LMBA, Université de Bretagne-Sud, BP 573, 56017 Vannes, France

Received by editor(s): October 2, 2016
Received by editor(s) in revised form: January 5, 2017
Published electronically: August 1, 2017
Communicated by: David Futer
Article copyright: © Copyright 2017 American Mathematical Society