The Yokonuma-Temperley-Lieb Algebra

Dimos Goundaroulis; Jesus Juyumaya; Aristides Kontogeorgis; Sofia Lambropoulou

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arXiv · 1012.1557

The Yokonuma-Temperley-Lieb Algebra

Dimos Goundaroulis·Jesus Juyumaya·Aristides Kontogeorgis·Sofia Lambropoulou

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Abstract

In this paper we introduce the Yokonuma-Temperley-Lieb algebra as a quotient of the Yokonuma-Hecke algebra over a two-sided ideal generated by an expression analogous to the one of the classical Temperley-Lieb algebra. The main theorem provides necessary and sufficient conditions for the Markov trace defined on the Yokonuma-Hecke algebra to pass through to the quotient algebra, leading to a sequence of knot invariants which coincide with the Jones polynomial.

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BibTeX RIS

Dimos Goundaroulis, Jesus Juyumaya, Aristides Kontogeorgis, Sofia Lambropoulou. 2013-12-06. The Yokonuma-Temperley-Lieb Algebra. https://arxiv.org/abs/1012.1557

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