YANG-BAXTER EQUATION, MAJORANA FERMIONS AND THREE BODY ENTANGLING STATES.

In this paper, we review some results obtained in our works with extension. The new type of braiding matrices called type-II has been extended to the solutions of Yang-Baxter equations (YBE). It is related to quantum entangling states. The four-dimensional realization is connected with Majorana fermions and the two-dimensional realization for the topological basis is the wigner DJ-function with J = 1/2. The YBE leads to the conclusion that the additivity rule of velocities for two anyons obeys Lorentz rather than Galilean. The discussion is extended to three body S-matrix formed by three two-body S-matrices. The three-qubit entanglement based on two-qubit entanglements is discussed. [ABSTRACT FROM AUTHOR]