Markov trace on a tower of affine Temperley-Lieb algebras of type $\tilde{A_{n}}$

Abstract

We define a tower of affine Temperley-Lieb algebras of type $\tilde{A_{n}}$. We prove that there exists a unique Markov trace on this tower, this trace comes from the Markov-Ocneanu-Jones trace on the tower of Temperley-Lieb algebras of type $A_{n}$.