G-旋模型中由正规子群确定的观测量代数的结构

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

设G是有限群,H是G的正规子群.本文考虑G-旋模型中由H确定的场代数F_H以及Hopf C*-代数D(H;G)在F_H上的作用,其中D(H;G)是量子double D(G)的子代数.首先,给出D(H;G)-不变子空间,即观测量代数A_((H,G))的具体结构.然后,利用迭代扭曲张量积,证明观测量代数A_((H,G))与···■H■G■H■G■H■···是C*-同构的,其中G表示G上复值函数空间,H表示群代数.

Let G be a finite group and H a normal subgroup. Starting from G-spin models, in which a field algebra 5vH 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 structure 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） is C＊-isomorphic to …… × H × G× H × G × H ×, where O denotes the algebra of complex functions on G, and H the group algebra.