The Yokonuma–Temperley–Lieb algebra
Volume 103 / 2014
Banach Center Publications 103 (2014), 77-99
MSC: 57M25, 20C08, 20F36.
DOI: 10.4064/bc103-0-3
Abstract
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.
