  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.
