C*-index of observable algebras in G-spin model

Abstract

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 A H in F is given. By constructing the quasi-basis of conditional expectation γ G of A H onto A G , the C*-index of γ G is exactly the index of H in G.