We define 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-3,
author = {D. Goundaroulis and J. Juyumaya and A. Kontogeorgis and S. Lambropoulou},
title = {The Yokonuma-Temperley-Lieb algebra},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {77-99},
zbl = {1336.57007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-3}
}
D. Goundaroulis; J. Juyumaya; A. Kontogeorgis; S. Lambropoulou. The Yokonuma-Temperley-Lieb algebra. Banach Center Publications, Tome 102 (2014) pp. 77-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-3/