Birman-Wenzl-Murakami Algebra and Topological Basis

【摘要】 In this paper,we use entangled states to construct 9 × 9-matrix representations of Temperley-Lieb algebra(TLA),then a family of 9× 9-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 ninedimensional BWMA into its three-dimensional counterpart.Finally,we find the topological basis states are spin singlet states in special case.更多还原

【Abstract】 In this paper,we use entangled states to construct 9 × 9-matrix representations of Temperley-Lieb algebra(TLA),then a family of 9× 9-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 ninedimensional BWMA into its three-dimensional counterpart.Finally,we find the topological basis states are spin singlet states in special case.更多还原