KMS在$C_c^{*}(\mathbb{N}^2)$上的状态

Pub Date : 2022-01-30 DOI:10.1017/S0017089523000071

Anbu Arjunan, Sruthymurali, S. Sundar

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引用次数: 2

摘要

摘要设$C_C^｛*｝（\mathbb｛N｝^｛2｝）$是区间投影可交换的等距$\｛v_｛（m，N）｝\，：\，m，N\in\mathbb{N｝\｝$的半群生成的泛$C^｛*}$代数。我们分析了由同态$C\，：\，\mathbb｛Z｝^｛2｝\ to \mathbb{R｝$确定的时间演化的$C_｛C｝^｝*｝（\mathbb｝N｝^2）$上的KMS态的结构。与简化版本$C_｛red｝^｛*｝（\mathbb｛N｝^{2｝）$相反，我们证明了$C_｛C｝^（*｝）上的KMS状态集具有丰富的结构。特别地，我们展示了无数类型I、II和III的极端KMS状态。

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KMS states on $C_c^{*}(\mathbb{N}^2)$

Abstract Let $C_c^{*}(\mathbb{N}^{2})$ be the universal $C^{*}$ -algebra generated by a semigroup of isometries $\{v_{(m,n)}\,:\, m,n \in \mathbb{N}\}$ whose range projections commute. We analyse the structure of KMS states on $C_{c}^{*}(\mathbb{N}^2)$ for the time evolution determined by a homomorphism $c\,:\,\mathbb{Z}^{2} \to \mathbb{R}$ . In contrast to the reduced version $C_{red}^{*}(\mathbb{N}^{2})$ , we show that the set of KMS states on $C_{c}^{*}(\mathbb{N}^{2})$ has a rich structure. In particular, we exhibit uncountably many extremal KMS states of type I, II and III.

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