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arXiv · 1110.4419

Birman-Wenzl-Murakami Algebra and the Topological Basis

Chengcheng Zhou·Kang Xue·Gangcheng Wang·Chunfang Sun·Guijiao Du
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Abstract

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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Chengcheng Zhou, Kang Xue, Gangcheng Wang, Chunfang Sun, Guijiao Du. 2011-10-20. Birman-Wenzl-Murakami Algebra and the Topological Basis. https://doi.org/10.1088/0253-6102%2F57%2F2%2F02

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