All Link Invariants for Two Dimensional Solutions of Yang-Baxter   Equation and Dressings
  All polynomial invariants of links for two dimensional solutions of Yang-Baxter equation is constructed by employing Turaev's method. As a consequence, it is proved that the best invariant so constructed is the Jones polynomial and there exist three solutions connecting to the Alexander polynomial. Invariants for higher dimensional solutions, obtained by the so-called dressings, are also investigated. It is observed that the dressings do not improve link invariant unless some restrictions are put on dressed solutions. 
N. Aizawa, M. Harada, M. Kawaguchi and E. Otsuki