摘要
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.
In two-dimensional lattice spin systems in which the spins take values in afinite group G,one can define a field algebra F which carries an action of a Hopf algebraD(G),the double algebra of G and moreover,an action of D(G;H),which is a subalgebraof D(G)determined by a subgroup H of G,so that F becomes a modular algebra.Theconcrete construction of D(G;H)-invariant subspace A_H in F is given.By constructingthe quasi-basis of conditional expectation γG of A_H onto A_G,the C~*-index of γG is exactlythe index of H in G.
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).
