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 , which is only a subalgebra of the quantum double D(G) of G. One can construct a C∗‐subalgebra of the field algebra of G‐spin models, such that is a D(H; G)‐module algebra. The concrete construction of D(H; G)‐invariant subalgebra of is given. Moreover, the C∗‐index of the conditional expectation from onto is calculated in terms of the quasi‐basis for zH.