Let F be the field algebra of G -spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G . The paper builds a correspondence between D(H) and th...Let F be the field algebra of G -spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G . The paper builds a correspondence between D(H) and the D(H) -invariant sub- C * -algebra A H in F, and proves that the correspondence is strictly monotonic.展开更多
Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by s...Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observable algebra A H, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that A H is a C *-algebra. The correspondence between H and A H is strictly monotonic. Finally, a duality between D(H) and A H is given via an irreducible vacuum C *-representation of F.展开更多
Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant su...Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.展开更多
In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action...In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action of D(G; H),which is a subalgebra of D(G) determined by a subgroup H of G,so that F becomes a modular algebra.The concrete construction of D(G; H)-invariant subspace AH in F is given.By constructing the quasi-basis of conditional expectation γG of AH onto AG,the C*-index of γG is exactly the index of H in G.展开更多
Polycrystalline BiFeO3 and rare earth substituted Bio.gRo.lFeO3 （BRFO, R=Y, Ho and Er） compounds were prepared by rapid solid state sintering technique. Structural phase analysis indicated that all the compounds sta...Polycrystalline BiFeO3 and rare earth substituted Bio.gRo.lFeO3 （BRFO, R=Y, Ho and Er） compounds were prepared by rapid solid state sintering technique. Structural phase analysis indicated that all the compounds stabilized in rhombohedral structure （R3c space group） and a small orthorhombic phase fraction was observed in BRFO compounds. From the Raman spectra results, the changes in the phonon frequencies （A1） and line widths suggested lattice distortion in the BRFO compounds as was evidenced in the XRD analysis. Compared to the linear variation of magnetization with magnetic field （M-H） shown by BFO, an obvious M-H loop was observed in BRFO compounds which could be due to the suppression of space modulated spin structure and was explained on the basis of weak ferromagnetism and field induced spin reorientation. UV-Vis spectroscopy evidenced a change in local FeO6 envi- ronment due to shift in the 6Alg→4T2g energy transition band. BRFO compounds with improved remnant magnetization and coercive field are applicable for magnetoelectric devices.展开更多
文摘Let F be the field algebra of G -spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G . The paper builds a correspondence between D(H) and the D(H) -invariant sub- C * -algebra A H in F, and proves that the correspondence is strictly monotonic.
基金Supported by the National Natural Science Foundationof China (No.10 0 0 10 2 0 )
文摘Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observable algebra A H, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that A H is a C *-algebra. The correspondence between H and A H is strictly monotonic. Finally, a duality between D(H) and A H is given via an irreducible vacuum C *-representation of F.
基金supported by National Science Foundation of China(10301004)
文摘Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.
基金supported by the National Natural Science Foundation of China(Grant.No.10301004)Basis Research Foundation of Beijing Institute of Technology(Grant No.200307A14).
文摘In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action of D(G; H),which is a subalgebra of D(G) determined by a subgroup H of G,so that F becomes a modular algebra.The concrete construction of D(G; H)-invariant subspace AH in F is given.By constructing the quasi-basis of conditional expectation γG of AH onto AG,the C*-index of γG is exactly the index of H in G.
基金supported by Department of Science and Technology (DST),Government of India under Fast Track Scheme (SR/FTP/PS-065/2011)
文摘Polycrystalline BiFeO3 and rare earth substituted Bio.gRo.lFeO3 （BRFO, R=Y, Ho and Er） compounds were prepared by rapid solid state sintering technique. Structural phase analysis indicated that all the compounds stabilized in rhombohedral structure （R3c space group） and a small orthorhombic phase fraction was observed in BRFO compounds. From the Raman spectra results, the changes in the phonon frequencies （A1） and line widths suggested lattice distortion in the BRFO compounds as was evidenced in the XRD analysis. Compared to the linear variation of magnetization with magnetic field （M-H） shown by BFO, an obvious M-H loop was observed in BRFO compounds which could be due to the suppression of space modulated spin structure and was explained on the basis of weak ferromagnetism and field induced spin reorientation. UV-Vis spectroscopy evidenced a change in local FeO6 envi- ronment due to shift in the 6Alg→4T2g energy transition band. BRFO compounds with improved remnant magnetization and coercive field are applicable for magnetoelectric devices.
