  The Temperley-Lieb algebra may be thought of as a quotient of the Hecke
algebra of type A, acting on tensor space as the commutant of the usual action
of quantum sl(2) on the n-th tensor power of the 2-dimensional irreducible
module. We define and study a quotient of the Birman-Wenzl-Murakami algebra,
which plays an analogous role for the 3-dimensional representation of quantum
sl(2). In the course of the discussion we prove some general results about the
radical of a cellular algebra, which may be of independent interest.
