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

Abstract

Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^{\ast }$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$, the concrete construction of the observable algebra ${\mathcal{A}}_{(H,G)}$ is given, as $D(H;G)$-invariant subspace. Furthermore, using the iterated twisted tensor product, one can prove that the observable algebra ${\mathcal{A}}_{(H,G)}=\cdots ⋊H⋊\hat{G}⋊H⋊\hat{G}⋊H⋊\cdots$, where $\hat{G}$ denotes the algebra of complex functions on $G$, and $H$ the group algebra.

12 pages

References in corpus (2)

• On Iterated Twisted Tensor Products of Algebras
• Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation