广义 Bunce-Deddens 代数及其 Toeplitz 扩张上的 KMS 态
算子代数
2015-10-14 v3
摘要
我们研究 Kribs 与 Solel 由有向图与正整数序列 构造的广义 Bunce-Deddens 代数及其 Toeplitz 扩张。我们用新的泛性质描述这两个 -代数，并证明它们的唯一性定理；若 决定一个无穷超自然数，则我们的广义 Bunce-Deddens 代数唯一性定理无需任何非周期性假设。当底层图有限时，我们计算 Toeplitz 代数中规范作用的 KMS 态。我们推得：广义 Bunce-Deddens 代数单当且仅当它恰支持一个 KMS 态，而这等价于序列 中的各项均与底层图的周期互素。
引用
@article{arxiv.1501.01712,
title = {KMS states on generalised Bunce-Deddens algebras and their Toeplitz extensions},
author = {David Robertson and James Rout and Aidan Sims},
journal= {arXiv preprint arXiv:1501.01712},
year = {2015}
}
备注
30 pages. This version includes a section on the topological graph $E(\infty)$, which allows us to use the work of Katsura to obtain a uniqueness theorem for $C^*(E,\omega)$, and a characterisation of the ideal structure of $C^*(E,\omega)$ when $E$ is finite and strongly connected. The introduction and references have been updated. Minor typos have been corrected