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arXiv · 1203.5922

Ribbon graphs and the Temperley-Lieb Algebra

Nafaa Chbili
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Abstract

Let $n$ be a nonnegative integer, we use ribbon $n-$graph diagrams and the Yamada polynomial skein relations to construct an algebra ${\mathcal Y}_n$ which is shown to be closely related to the Temerley-Lieb Algebra. We prove that the algebra ${\mathcal Y}_2$ is isomorphic to some quotient of a three variables polynomial algebra. Then, we give a family of generators for the algebra ${\mathcal Y}_3$.

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Nafaa Chbili. 2012-03-27. Ribbon graphs and the Temperley-Lieb Algebra. https://arxiv.org/abs/1203.5922

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