  We propose a framization of the Temperley-Lieb algebra. The framization is a
procedure that can briefly be described as the adding of framing to a known
knot algebra in a way that is both algebraically consistent and topologically
meaningful. Our framization of the Temperley-Lieb algebra is defined as a
quotient of the Yokonuma-Hecke 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. Using this we construct
1-variable invariants for classical knots and links, which, as we show, are not
topologically equivalent to the Jones polynomial.
