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
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.
