C^∗‐index of observable algebra in the field algebra determined by a normal group

Abstract

Let G be a finite group and H a normal subgroup. By D(H; G), we denote the crossed product of C(H) and CG, which is only a subalgebra of the quantum double D(G) of G. One can construct a C * -subalgebra  H of the field algebra  of G-spin models, such that  H is a D(H; G)-module algebra. The concrete construction of D(H; G)-invariant subalgebra  (H,G) of  H is given. Moreover, the C * -index of the conditional expectation z H from  H onto  (H,G) is calculated in terms of the quasi-basis for z H .