$C^*$ -可观测代数在由正规群确定的域代数中的指数
$C^*$-index of observable algebra in the field algebra determined by a normal group
摘要：
设$G$是有限群，$H$是正规子群。$D(H;G)$是$C(H)$和${\Bbb C}G$的交叉积，而$D(G)$是$G$的量子二重数。可以构造$G$ -自旋模型的场代数$\mathcal{F}$的$C^*$ -子代数${\mathcal{F}}_{_H}$，使得${\mathcal{F}}_{_H}$是$D(H;G)$ -模代数.给出了${\mathcal{F}}_{_H}$的$D(H;G)$不变子代数${\mathcal{A}}_{_{(H,G)}}$的具体构造.通过构造${\mathcal{F}}_{_H}$的条件期望$z_{_H}$到${\mathcal{A}}_{_{(H,G)}}$上的拟基，给出了$z_{_H}$的$C^*$ -指标.
英文摘要：
Let $G$ be a finite group and $H$ a normal subgroup. $D(H;G)$ is the crossed product of $C(H)$ and ${\Bbb C}G$ which is only a subalgebra of $D(G)$, the quantum double of $G$. One can construct a $C^*$-subalgebra ${\mathcal{F}}_{_H}$ of the field algebra $\mathcal{F}$ of $G$-spin models, such that ${\mathcal{F}}_{_H}$ is a $D(H;G)$-module algebra. The concrete construction of $D(H;G)$-invariant subalgebra ${\mathcal{A}}_{_{(H,G)}}$ of ${\mathcal{F}}_{_H}$ is given. By constructing the quasi-basis of conditional expectation $z_{_H}$ of ${\mathcal{F}}_{_H}$ onto ${\mathcal{A}}_{_{(H,G)}}$, the $C^*$-index of $z_{_H}$ is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
