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arXiv · 1708.02014

Framization of a Temperley-Lieb algebra of type $\mathtt{B}$

Marcelo Flores·Dimos Goundaroulis
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Abstract

We extend the Framization of the Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$. We first define a natural extension of the classical Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$ and prove that such an extension supports a unique linear Markov trace function. We then introduce the Framization of the Temperley-Lieb algebra of type $\mathtt{B}$ as a quotient of the Yokonuma-Hecke algebra of type $\mathtt{B}$. The main theorem provides necessary and sufficient conditions for the Markov trace defined on the Yokonuma-Hecke algebra of type $\mathtt{B}$ to pass to the quotient algebra. Using the main theorem, we construct invariants for framed links and classical links inside the solid torus.

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Marcelo Flores, Dimos Goundaroulis. 2017-08-07. Framization of a Temperley-Lieb algebra of type $\mathtt{B}$. https://arxiv.org/abs/1708.02014

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