Exactly Solvable Models and New Link Polynomials. V. Yang-Baxter Operator and Braid-Monoid Algebra

Abstract

Yang-Baxter operator is shown to be a fundamental object which relates theory of solvable models to theory of knots and links. First, general properties of Yang-Baxter operators are investigated. Second, a method to construct composite Yang-Baxter operators is explicitly shown. Lastly, from Yang-Baxter operators with crossing symmetry, braid-monoid algebras are derived. It is emphasized that the factorized S -matrices and their graphical illustrations link two approaches, algebraic and combinatorial, in the knot theory.