A survey on Temperley-Lieb-type quotients from the Yokonuma-Hecke algebras
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Publication:1697065
DOI10.1007/978-3-319-68103-0_2zbMATH Open1388.20012arXiv1611.00537OpenAlexW2964258621WikidataQ59869591 ScholiaQ59869591MaRDI QIDQ1697065
Publication date: 15 February 2018
Abstract: In this survey we collect all results regarding the construction of the Framization of the Temperley-Lieb algebra of type as a quotient algebra of the Yokonuma-Hecke algebra of type . More precisely, we present all three possible quotient algebras the emerged during this construction and we discuss their dimension, linear bases, representation theory and the necessary and sufficient conditions for the unique Markov trace of the Yokonuma-Hecke algebra to factor through to each one of them. Further, we present the link invariants that are derived from each quotient algebra and we point out which quotient algebra provides the most natural definition for a framization of the Temperley-Lieb algebra. From the Framization of the Temperley-Lieb algebra we obtain new one-variable invariants for oriented classical links that, when compared to the Jones polynomial, they are not topologically equivalent since they distinguish more pair of non isotopic oriented links. Finally, we discuss the generalization of the newly obtained invariants to a new two-variable invariant for oriented classical links that is stronger than the Jones polynomial.
Full work available at URL: https://arxiv.org/abs/1611.00537
Related Items (2)
The Yokonuma–Temperley–Lieb algebra ⋮ Framization of Schur-Weyl duality and Yokonuma-Hecke type algebras
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