Ribbon Graphs and Temperley-Lieb Algebra

Abstract

Let n be a nonnegative integer, we use ribbon n−graph diagrams and the Yamada polynomial skein relations to construct an algebra Y n which is shown to be closely related to the Temerley-Lieb Algebra. We prove that the algebra Y 2 is isomorphic to some quotient of a three variables polynomial algebra. Then, we give a family of generators for the algebra Y 3 .