We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of...We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of Yang-Baxter equation.A unitary matrix R(x,φ1,φ2)is generated via the Yang-Baxterization approach.Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x,φ1,φ2).Berry phase of this Yang-Baxter system is investigated in detail.展开更多
The notion of weak Doi-Hopf π-datum and weak Doi-Hopf π-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (B?hm, 2000), also as a generalization of a Doi-H...The notion of weak Doi-Hopf π-datum and weak Doi-Hopf π-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (B?hm, 2000), also as a generalization of a Doi-Hopf π-module in- troduced in (Wang, 2004). Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopf π-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.展开更多
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 pr...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.展开更多
Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are deter...Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.展开更多
基金Supported by National Natural Science Foundation of China under Grants No.10875026
文摘We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of Yang-Baxter equation.A unitary matrix R(x,φ1,φ2)is generated via the Yang-Baxterization approach.Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x,φ1,φ2).Berry phase of this Yang-Baxter system is investigated in detail.
基金Project supported by the Program for New Century Excellent Talents in University (No. 04-0522), the National Science Foundation of Zhejiang Province of China (No. 102028), and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 704004)
文摘The notion of weak Doi-Hopf π-datum and weak Doi-Hopf π-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (B?hm, 2000), also as a generalization of a Doi-Hopf π-module in- troduced in (Wang, 2004). Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopf π-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.
基金Supported by National Natural Science Foundation of China under Grant No. 10875026
文摘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.
文摘Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.
