The construction of observable algebra in field algebra of G-spin models determined by a normal subgroup

2015/05/22 by Xin Qiaoling, Qiaoling, Xin, Lining Jiang +2
Mathematics · Physics and Astronomy · #16T05 #46L40 #46N50 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Quantum many-body systems #math-ph #math.MP #math.OA #math.QA #msc:16T05 #msc:46L40 #msc:46N50

paper · pdf · doi:10.48550/arxiv.1505.06051

12 pages

arxiv created 2015/05/22 · openalex publication_date 2015/05/22 · arxiv updated 2015/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let G be a finite group and H a normal subgroup. Starting from G-spin models, in which a non-Abelian field F_H w.r.t. H carries an action of the Hopf C^*-algebra D(H;G), a subalgebra of the quantum double D(G), the concrete construction of the observable algebra A_(H,G) is given, as D(H;G)-invariant subspace. Furthermore, using the iterated twisted tensor product, one can prove that the observable algebra A_(H,G)=⋯\rtimes H\rtimesG\rtimes H\rtimesG\rtimes H\rtimes⋯, where G denotes the algebra of complex functions on G, and H the group algebra.

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