论文标题
Ryll-Nardzewski定理在汽车代数上的失败
Failure of the Ryll-Nardzewski theorem on the CAR algebra
论文作者
论文摘要
一系列随机变量的传播性是一种分布对称性，通过$ \ mathbb {j} _ \ mathbb {z} $的合适动作实现，这是$ \ m athbb {z} $的unitial semigroup，cofinite范围都严格增加地图。我们表明，$ \ mathbb {j} _ \ mathbb {z} $是可正常的，但不正确，尽管它确实接受了正确的folner序列。这使我们能够证明在汽车代数$ {\ rm car}（\ mathbb {z}）$上存在无法交换的可涂抹状态。此外，我们还表明，在$ {\ rm car}（\ mathbb {z}）$上存在无法传播的固定状态。
Spreadability of a sequence of random variables is a distributional symmetry that is implemented by suitable actions of $\mathbb{J}_\mathbb{Z}$, the unital semigroup of strictly increasing maps on $\mathbb{Z}$ with cofinite range. We show that $\mathbb{J}_\mathbb{Z}$ is left amenable but not right amenable, although it does admit a right Folner sequence. This enables us to prove that on the CAR algebra ${\rm CAR}(\mathbb{Z})$ there exist spreadable states that fail to be exchangeable. Moreover, we also show that on ${\rm CAR}(\mathbb{Z})$there exist stationary states that fail to be spreadable.
