Other quantum relatives of the Alexander polynomial through the Links-Gould invariants
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- by Ben-Michael Kohli and Bertrand Patureau-Mirand PDF
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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 $U_q\mathfrak {gl}(1|1)$. In this paper, we show these Hopf algebras share properties with the $-1$ specialization of $U_q\mathfrak {gl}(n|1)$ leading to the proof of a conjecture by David De Wit, Atsushi Ishii and Jon Links on the Links-Gould invariants.References
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Additional Information
- Ben-Michael Kohli
- Affiliation: IMB UMR5584, CNRS, Université Bourgogne Franche-Comté, F-21000 Dijon, France
- MR Author ID: 1151093
- Email: Ben-Michael.Kohli@u-bourgogne.fr
- Bertrand Patureau-Mirand
- Affiliation: UMR 6205, LMBA, Université de Bretagne-Sud, BP 573, 56017 Vannes, France
- Email: bertrand.patureau@univ-ubs.fr
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5419-5433
- MSC (2010): Primary 57M27; Secondary 17B37
- DOI: https://doi.org/10.1090/proc/13699
- MathSciNet review: 3717968