The Yokonuma-Hecke algebras and the HOMFLYPT polynomial

Maria Chlouveraki, Sofia Lambropoulou

Published 2012-04-09, updated 2013-11-28Version 4

We compare the invariant for classical knots and links defined using the Juyumaya trace on the Yokonuma-Hecke algebras with the HOMFLYPT polynomial. We show that the two invariants, as maps on the set ${\mathcal L}$ of oriented link types in $S^3$, do not coincide except in a few trivial cases.