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

Abstract

Let $G$ be a finite group. Starting from the field algebra $\mathcal{F}$ of $G$-spin models, one can construct the crossed product $C^{\ast }$-algebra $\mathcal{F}⋊D(G)$ such that it coincides with the $C^{\ast }$-basic construction for the field algebra $\mathcal{F}$ and the $D(G)$-invariant subalgebra of $\mathcal{F}$, where $D(G)$ is the quantum double of $G$. Under the natural $\widehat{D(G)}$-module action on $\mathcal{F}⋊D(G)$,the iterated crossed product $C^{\ast }$-algebra can be obtained, which is $C^{\ast }$-isomorphic to the $C^{\ast }$-basic construction for $\mathcal{F}⋊D(G)$ and the field algebra $\mathcal{F}$. Furthermore, one can show that the iterated crossed product $C^{\ast }$-algebra is a new field algebra and give the concrete structure with the order and disorder operators.

14 pages

References in corpus (2)

• Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation
• $C^{\ast }$-index of observable algebra in the field algebra determined by a normal group