Markov elements in affine Temperley-Lieb algebras
Group Theory
2015-01-28 v1
Abstract
We define a tower of affine Temperley-Lieb algebras of type and we define Markov elements in those algebras. We prove that any trace over an affine Temperley-Lieb algebras of type is uniquely defined by its values on the Markov elements.
Cite
@article{arxiv.1501.06756,
title = {Markov elements in affine Temperley-Lieb algebras},
author = {Sadek Al Harbat},
journal= {arXiv preprint arXiv:1501.06756},
year = {2015}
}
Comments
We proved in arXiv:1311.7092 that any trace over an affine Temperley-Lieb algebras of type $\tilde{A_{n}}$ is uniquely defined by its values on the Markov elements, for $n\ge 3$. We here provide the proof for $n=2$ for completeness