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

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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.

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  1. Department of Mathematics, Beijing Institute of Technology, 100081, Beijing, China

    Lining Jiang

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  1. Lining Jiang
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Correspondence to Lining Jiang.

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Jiang, L. C*-index of observable algebras in G-spin model. Sci. China Ser. A-Math. 48, 57–66 (2005). https://doi.org/10.1360/03ys0119

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