C^*-index of observable algebra in the field algebra determined by a normal group

2015/05/17 by Qiaoling, Xin, Lining Jiang, Lining, Jiang · 1 citation
Mathematics · #16S35 #46L05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1505.04784

openalex publication_date 2015/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group and H a normal subgroup. D(H;G) is the crossed product of C(H) and \Bbb CG which is only a subalgebra of D(G), the quantum double of G. One can construct a C^*-subalgebra F_H of the field algebra F of G-spin models, such that F_H is a D(H;G)-module algebra. The concrete construction of D(H;G)-invariant subalgebra A__(H,G) of F_H is given. By constructing the quasi-basis of conditional expectation z_H of F_H onto A__(H,G), the C^*-index of z_H is given.

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• Jones type basic construction on field algebras of G-spin models

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