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

2016/06/08 by Kohli, Ben-Michael, Patureau-Mirand, Bertrand · 3 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1606.02538

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.

Cited by

• U_q(\mathfrakgl(m|n)) bounds on the minimal genus of virtual links
• On some log-concavity properties of the Alexander-Conway and Links-Gould invariants
• On the colored Links--Gould polynomial

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