Framization of a Temperley-Lieb algebra of type
arXiv:1708.02014
Abstract
We extend the Framization of the Temperley-Lieb algebra to Coxeter systems of type . We first define a natural extension of the classical Temperley-Lieb algebra to Coxeter systems of type 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 as a quotient of the Yokonuma-Hecke algebra of type . The main theorem provides necessary and sufficient conditions for the Markov trace defined on the Yokonuma-Hecke algebra of type to pass to the quotient algebra. Using the main theorem, we construct invariants for framed links and classical links inside the solid torus.
22 pages, 4 figures