论文标题
KMS状态在$ C_C^{*}（\ Mathbb {n}^2）$
KMS states on $C_c^{*}(\mathbb{N}^2)$
论文作者
论文摘要
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.我们分析了$ c_ {c}^{*}（\ Mathbb {n}^2）$在$ c_ {c}^{*}上的kms状态的结构。与还原版本$ C_ {RED}^{*}（\ Mathbb {n}^{2}）$相反，我们表明$ C_ {C}^{*}上的kms nates nates nates nates（\ Mathbb {n}^{2}^{2}）$具有丰富的结构。特别是，我们表现出许多极端的I型，II和III型的极端国公里。
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.
