Birman-Wenzl-Murakami Algebra and the Topological Basis

Details Birman-Wenzl-Murakami Algebra and the Topological Basis Birman-Wenzl-Murakami Algebra and the Topological Basis

2011-10-20

arxiv.org/abs/1110.4419v1

Physics

Quantum Physics

11pages, 1 figure

Scientific paper

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.

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