The Yokonuma-Hecke algebras and the HOMFLYPT polynomial
  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. 
Maria Chlouveraki, Sofia Lambropoulou
math.GT