  In this paper, we use entangled states to construct 9x9-matrix
representations of Temperley-Lieb algebra (TLA), then a family of 9x9-matrix
representations of Birman-Wenzl-Murakami algebra (BWMA) have been presented.
Based on which, three topological basis states have been found. And we apply
topological basis states to recast nine-dimensional BWMA into its
three-dimensional counterpart. Finally, we find the topological basis states
are spin singlet states in special case.
