The Pure Yang-Baxter Equation And Link Invariants

In Reference [3], there constructs the complex 2~N dimensional matrix representationsof the braid group B_N by using the solutions of the pure Yang-Baxter equation accordingto the generalized Jones method , constructs the Markov trace and then obtains the JonesPolynomial. The key of the generalized Jones method is how to construct the representations ofthe braid group and the Markov trace from the relation between the solutions of the pureYang-Baxter equation and the braid group . Indeed we construct a new equation similarto the pure Yang-Baxter equation, construct the representations of the braid group andthe Markov trace and then obtain the multi-variable link polynomials. For the solutions of the pure Yang-Baxter equation are included in those of the newequation , the link polynomials coming from the new equation can include the link poly-nomials constructed by the pure Yang-Baxter equation.